To study the effect of long chain molecule and surface active agent on non-Newtonianfluid properties, rheological experiments on two different fluids have been done. The first group of the fluid is the hydroxyethyl cellulose water solution, and the second is the water solution containing the mixture of dodecyltriethyl ammonium bromide and lauryl sodium sulfate. With the increasing shear rate, shear thinning phenomenon appears in the first group of solution, and a special shear thickening-shear thinning phenomenon appears in the second group. It is considered that the special rheological phenomenon is caused by the difference between the aggregating and the departing speed of the colloidal particles formed in the fluid. The difference between the two speeds relates with the shear rate. The experiment results indicate that the rheological properties can be designed by choosing proper additives at a certain shear rate, and such a fluid with special viscosity variation should be included in the classification of the non-Newtonianfluid.

To study the effect of long chain molecule and surface active agent on non-Newtonianfluid properties, rheological experiments on two different fluids have been done. The first group of the fluid is the hydroxyethyl cellulose water solution, and the second is the water solution containing the mixture of dodecyl- triethyl ammonium bromide and lauryl sodium sulfate. With the increasing shear rate, shear thinning phenomenon appears in the first group of solution, and a spe- cial shear thickening-shear thinning phenomenon appears in the second group. It is considered that the special rheological phenomenon is caused by the difference between the aggregating and the departing speed of the colloidal particles formed in the fluid. The difference between the two speeds relates with the shear rate. The experiment results indicate that the rheological properties can be designed by choosing proper additives at a certain shear rate, and such a fluid with special vis- cosity variation should be included in the classification of the non-Newtonianfluid.

In this work, the microconfined shear deformation of a droplet in an equiviscous non-Newtonian immiscible fluid is investigated by modeling and experiments. A phenomenological model based on the assumption of ellipsoidal shape and taking into account wall effects is proposed for systems made of non-Newtonian second-order fluids. The model, without any adjustable parameters, is tested by comparison with experiments under simple shear flow performed in a sliding plate apparatus, where the ratio between the distance between the confining walls and the droplet radius can be varied. The agreement between model predictions and experimental data is good both in steady state shear and in transient drop retraction upon cessation of flow. The results obtained in this work are relevant for microfluidics applications where non-Newtonianfluids are used.

This book gives a brief but thorough introduction to the fascinating subject of non-Newtonianfluids, their behavior and mechanical properties. After a brief introduction of what characterizes non-Newtonianfluids in Chapter 1 some phenomena characteristic of non-Newtonianfluids are presented in Chapter 2. The basic equations in fluid mechanics are discussed in Chapter 3. Deformation kinematics, the kinematics of shear flows, viscometric flows, and extensional flows are the topics in Chapter 4. Material functions characterizing the behavior of fluids in special flows are defined in Chapter 5. Generalized Newtonian fluids are the most common types of non-Newtonianfluids and are the subject in Chapter 6. Some linearly viscoelastic fluid models are presented in Chapter 7. In Chapter 8 the concept of tensors is utilized and advanced fluid models are introduced. The book is concluded with a variety of 26 problems. Solutions to the problems are ready for instructors.

The coalescence of two initially stationary droplets of shear-thinning fluids in a gaseous environment is investigated numerically using the lattice Boltzmann method, with particular interest in non-Newtonian flow effects on the internal mixing subsequent to coalescence. Coalescence of equal-sized droplets, with one being Newtonian while the other is non-Newtonian, leads to the non-Newtonian droplet wrapping around the Newtonian one and hence minimal fine-scale mixing. For unequal-sized droplets, mixing is greatly promoted if both droplets are shear-thinning. When only one of the droplets is shear-thinning, the non-Newtonian effect from the smaller droplet is found to be significantly more effective than that from the larger droplet in facilitating internal jetlike mixing. Parametric study with the Carreau-Yasuda model indicates that the phenomena are universal to a wide range of shear-thinning fluids, given that the extent of shear thinning reaches a certain level, and the internal jet tends to be thicker and develops more rapidly with increasing extent of the shear-thinning effect.

This work presents a comprehensive review of electrokinetics pertaining to non-Newtonianfluids. The topic covers a broad range of non-Newtonian effects in electrokinetics, including electroosmosis of non-Newtonianfluids, electrophoresis of particles in non-Newtonianfluids, streaming potential effect of non-Newtonianfluids and other related non-Newtonian effects in electrokinetics. Generally, the coupling between non-Newtonian hydrodynamics and electrostatics not only complicates the electrokinetics but also causes the fluid/particle velocity to be nonlinearly dependent on the strength of external electric field and/or the zeta potential. Shear-thinning nature of liquids tends to enhance electrokinetic phenomena, while shear-thickening nature of liquids leads to the reduction of electrokinetic effects. In addition, directions for the future studies are suggested and several theoretical issues in non-Newtonian electrokinetics are highlighted.

We study the existence of weak solution for unsteady fluid-structure interaction problem for shear-thickening flow. The time dependent domain has at one part a flexible elastic wall. The evolution of fluid domain is governed by the generalized string equation with action of the fluid forces. The power-law viscosity model is applied to describe shear-dependent non-Newtonianfluids.

To investigate the microstructural evolution dependency on the apparent viscosity in shear-thickening fluids (STFs), a hybrid mesoscale model combined with stochastic rotation dynamics (SRD) and molecular dynamics (MD) is used. Muller-Plathe reverse perturbation method is adopted to analyze the viscosities of STFs in a two-dimensional model. The characteristic of microstructural evolution of the colloidal suspensions under different shear rate is studied. The effect of diameter of colloidal particles and the phase volume fraction on the shear thickening behavior is investigated. Under low shear rate, the two-atom structure is formed, because of the strong particle attractions in adjacent layers. At higher shear rate, the synergetic pair structure extends to layered structure along flow direction because of the increasing hydrodynamics action. As the shear rate rises continuously, the layered structure rotates and collides with other particles, then turned to be individual particles under extension or curve string structure under compression. Finally, at the highest shear rate, the strings curve more severely and get into two-dimensional cluster. The apparent viscosity of the system changes from shear-thinning behavior to the shear-thickening behavior. This work presents valuable information for further understanding the shear thickening mechanism.

We present a theoretical scheme to calculate the electrophoretic motion of charged colloidal particles immersed in complex (non-Newtonian) fluids possessing shear-rate-dependent viscosities. We demonstrate that this non-Newtonian rheology leads to an explicit shape and size dependence of the electrophoretic velocity of a uniformly charged particle in the thin-Debye-layer regime, in contrast to electrophoresis in Newtonian fluids. This dependence is caused by non-Newtonian stresses in the bulk (electroneutral) fluid outside the Debye layer, whose magnitude is naturally characterized in an electrophoretic Deborah number.

Wall shear stress has been measured by flush-mounted hot film anemometry distal to an Ionescu-Shiley tri-leaflet valve under pulsatile flow conditions. Both Newtonian (aqueous glycerol) and non-Newtonian (aqueous polyacrylamide) blood analog fluids were investigated. Significant differences in the axial distribution of wall shear stress between the two fluids are apparent in flows having nearly identical Reynolds numbers. The Newtonian fluid exhibits a (peak) wall shear rate which is maximized near the valve seat (30 mm) and then decays to a fully developed flow value (by 106 mm). In contrast, the shear rate of the non-Newtonianfluid at 30 mm is less than half that of the Newtonian fluid and at 106 mm is more than twice that of the Newtonian fluid. It is suggested that non-Newtonian rheology influences valve flow patterns either through alterations in valve opening associated with low shear separation zones behind valve leaflets, or because of variations in the rate of jet spreading. More detailed studies are required to clarify the mechanisms. The Newtonian wall shear stresses for this valve are low. The highest value observed anywhere in the aortic chamber was 2.85 N/m2 at a peak Reynolds number of 3694.

New types of robots inspired by biological principles of assembly, locomotion, and behavior have been recently described. In this work we explored the concept of robots that are based on more fundamental physical phenomena, such as fluid dynamics, and their potential capabilities. We report a robot made entirely of non-Newtonianfluid, driven by shear strains created by spatial patterns of audio waves. We demonstrate various robotic primitives such as locomotion and transport of metallic loads-up to 6-fold heavier than the robot itself-between points on a surface, splitting and merging, shapeshifting, percolation through gratings, and counting to 3. We also utilized interactions between multiple robots carrying chemical loads to drive a bulk chemical synthesis reaction. Free of constraints such as skin or obligatory structural integrity, fluid robots represent a radically different design that could adapt more easily to unfamiliar, hostile, or chaotic environments and carry out tasks that neither living organisms nor conventional machines are capable of.

Dimensional analysis has been applied to an unsteady pulsatile flow of a shear-thinning power-law non-Newtonian liquid. An experiment was then designed in which both Newtonian and non-Newtonian liquids were used to model blood flow through a large-scale (38.5 mm dia.), simplified, rigid arterial junction (a distal anastomosis of a femorodistal bypass). The flow field within the junction was obtained by Particle Imaging Velocimetry and near-wall velocities were used to calculate the wall shear stresses. Dimensionless wall shear stresses were obtained at different points in the cardiac cycle for two different but dynamically similar non-Newtonianfluids; the good agreement between the measured dimensionless wall shear stresses confirm the validity of the dimensional analysis. However, blood exhibits a constant viscosity at high-shear rates and to obtain complete dynamic similarity between large-scale experiments and life-scale flows, the high-shear viscosity also needs to be included in the analysis. How this might be done is discussed in the paper.

The paper presents analytical solution for hydraulic fracture driven by a non-Newtonianfluid and propagating under plane strain conditions in cross sections parallel to the fracture front. Conclusions are drawn on the influence of the fluid properties on the fracture propagation.

Owing to frequent processing of biofluids in Lab-on-a-chip microfluidic devices, electroosmotic mobilities of non-Newtonianfluids are investigated numerically. The general Cauchy momentum equation governing the electroosmotic velocity is simplified by incorporation of the Gouy-Chapman solution of the Poisson-Boltzmann equation and the Carreau fluid constitutive model. Then the finite element method for solving the simplified version of Cauchy momentum equation is validated through comparisons with two exact solutions, i.e., Newtonian fluids and power-law fluids. Analyses shows that different from Newtonian fluids with a constant dimensionless electroosmotic mobility of unit one, dimensionless electroosmotic mobilities for non-Newtonian Carreau fluids are dependent on four dimensionless groups, such as dimensionless surface zeta potential , Weissenberg number Wi, fluid power-law exponent n and transitional parameter {\\beta}. It is found out that with increasing and decreasing of n and {\\beta}, electroosmotic ...

The development of the viscous fingering instability in Hele-Shaw cells has great practical and scientific importance. Recently, researchers have proposed different strategies to control the number of interfacial fingering structures, or to minimize as much as possible the amplitude of interfacial disturbances. Most existing studies address the situation in which an inviscid fluid displaces a viscous Newtonian fluid. In this work, we report on controlling and minimizing protocols considering the situation in which the displaced fluid is a non-Newtonian, power-law fluid. The necessary changes on the controlling schemes due to the shear-thinning and shear thickening nature of the displaced fluid are calculated analytically and discussed.

We show that relativistic fluids behave as non-Newtonianfluids. First, we discuss the problem of acausal propagation in the diffusion equation and introduce the modified Maxwell-Cattaneo-Vernotte (MCV) equation. By using the modified MCV equation, we obtain the causal dissipative relativistic (CDR) fluid dynamics, where unphysical propagation with infinite velocity does not exist. We further show that the problems of the violation of causality and instability are intimately related, and the relativistic Navier-Stokes equation is inadequate as the theory of relativistic fluids. Finally, the new microscopic formula to calculate the transport coefficients of the CDR fluid dynamics is discussed. The result of the microscopic formula is consistent with that of the Boltzmann equation, i.e., Grad's moment method.

A steady-state analysis is conducted to examine the basic flow structure of a non-Newtonianfluid in a domain including an inflow region, a contraction region, and an outflow region. A Cartesian grid system is used throughout the entire flow domain, including the contraction region, thus creating an irregular grid cell structure adjacent to the curved boundary. At node points adjacent to the curved boundary symmetry conditions are derived for the different flow variables in order to solve the governing difference equations. Attention is given to the motion and non-Newtonian constitutive equations, the boundary conditions, the numerical modeling of the non-Newtonian equations, the stream function contour lines for the non-Newtonianfluid, the vorticity contour lines for the non-Newtonianfluid, the velocity profile across the contraction, and the shear stress contour lines for the non-Newtonianfluid.

We examine various aspects of dynamic wetting with viscous Newtonian and non-Newtonianfluids. Rather than concentrating on the mechanisms that relieve the classic contact line stress singularity, we focus on the behavior in the wedge flow near the contact line which has the dominant influence on wetting with these fluids. Our experiments show that a Newtonian polymer melt composed of highly flexible molecules exhibits dynamic wetting behavior described very well by hydrodynamic models that capture the critical properties of the Newtonian wedge flow near the contact line. We find that shear thinning has a strong impact on dynamic wetting, by reducing the drag of the solid on the fluid near the contact line, while the elasticity of a Boger fluid has a weaker impact on dynamic wetting. Finally, we find that other polymeric fluids, nominally Newtonian in rheometric measurements, exhibit deviations from Newtonian dynamic wetting behavior.

The paper contains results of the experimental study on atomization process of aqueous solutions of glycerol and aqueous solutions of glycerol-polyacrylamide (Rokrysol WF1) in an ultrasonic inhaler. In experiments the different concentration aqueous solutions of glycerol and glycerol-polyacrylamide have been tested. The results have been obtained by the use of laser diffraction technique. The differences between characteristics of ultrasonic atomization for test liquids have been observed. The analysis of drop size histograms shows that the different sizes of drops have been formed during atomization process. The present study confirmed the previous reports which suggested that the drops size changes with the increase in viscosity of solution changes in spray characteristics were also observed. It has been shown that the shear and extensional viscosities affect the process of atomization.

Full Text Available Non-Newtonianfluids, such as polymer solutions, have been used by the oil industry for many years as fracturing agents and drilling mud. These solutions, which normally include thickened water and jelled fluids, are injected into the formation to enhanced oil recovery by improving sweep efficiency. It is worth noting that some heavy oils behave non-Newtonianly. Non-Newtonianfluids do not have direct proportionality between applied shear stress and shear rate and viscosity varies with shear rate depending on whether the fluid is either pseudoplastic or dilatant. Viscosity decreases as shear rate increases for the former whilst the reverse takes place for dilatants. Mathematical models of conventional fluids thus fail when applied to non-Newtonianfluids. The pressure derivative curve is introduced in this descriptive work for a dilatant fluid and its pattern was observed. Tiab’s direct synthesis (TDS methodology was used as a tool for interpreting pressure transient data to estimate effective permeability, skin factors and non-Newtonian bank radius. The methodology was successfully verified by its application to synthetic examples. Also, comparing it to pseudoplastic behavior, it was found that the radial flow regime in the Newtonian zone of dilatant fluids took longer to form regarding both the flow behavior index and consistency factor.

Although blood is known to have shear-thinning and viscoelastic properties, the effects of such properties on the hemodynamic characteristics in various vascular environments are not fully understood yet. For a quantitative hemodynamic analysis, the refractive index of a transparent blood analogue needs to be matched with that of the flowing conduit in order to minimize the errors according to the distortion of the light. In this study, three refractive index-matched blood analogue fluids with different viscosities are prepared—one Newtonian and two non-Newtonian analogues—which correspond to healthy blood with 45 % hematocrit (i.e., normal non-Newtonian) and obese blood with higher viscosity (i.e., abnormal non-Newtonian). The effects of the non-Newtonian rheological properties of the blood analogues on the hemodynamic characteristics in the post-stenosis region of an axisymmetric stenosis model are experimentally investigated using particle image velocimetry velocity field measurement technique and pathline flow visualization. As a result, the centerline jet flow from the stenosis apex is suppressed by the shear-thinning feature of the blood analogues when the Reynolds number is smaller than 500. The lengths of the recirculation zone for abnormal and normal non-Newtonian blood analogues are 3.67 and 1.72 times shorter than that for the Newtonian analogue at Reynolds numbers smaller than 200. The Reynolds number of the transition from laminar to turbulent flow for all blood analogues increases as the shear-thinning feature increases, and the maximum wall shear stresses in non-Newtonianfluids are five times greater than those in Newtonian fluids. However, the shear-thinning effect on the hemodynamic characteristics is not significant at Reynolds numbers higher than 1000. The findings of this study on refractive index-matched non-Newtonian blood analogues can be utilized in other in vitro experiments, where non-Newtonian features dominantly affect the flow

A solution for the two-dimensional and axisymmetric laminar boundary-layer momentum equation of power-law non-Newtonianfluid is presented. The analysis makes use of the Merk-Chao series solution method originally devised for the flow of Newtonian fluid. The universal functions for the leading term in the series are tabulated for n from 0.2 to 2. Equations governing the universal functions associated with the second and the third terms are provided. The solution together with either Lighthill's formula or Chao's formula constitutes a simple yet general procedure for the calculation of wall shear and surface heat transfer rate. The theory was applied to flows over a circular cylinder and a sphere and the results compared with published data.

Along with Newtonian fluids (for example, water), fluids with non-Newtonian rheology are widespread in nature and industry. The characteristic feature of a non-Newtonianfluid is the non-linear dependence between the shear stress and shear rate tensors. The form of this relation defines the types of non-Newtonian behavior: viscoplastic, pseudoplastic, dilatant and viscoelastic. The present work is devoted to the study of the Rayleigh-Taylor instability in pseudoplastic fluids. The main aim of the work is to undertake a direct three-dimensional numerical simulation of the mixing of two media with various rheologies and obtain the width of the mixing layer and the kinetic energy spectra, depending on the basic properties of the shear thinning liquids and the Atwood number. A theoretical study is carried out on the basis of the Navier-Stokes equation system for weakly compressible media.

. Validation of the CFD model was made against LDA tangential velocity measurements (error less than 8 %) using water a fluid. The shear stress over the membrane surface was inferred from the CFD simulations for water. However, activated sludge is a non-Newtonian liquid, for which the CFD model was modified...... incorporating the non-Newtonian behaviour of activated sludge. Shear stress and area-weighted average shear stress relationships were made giving error less that 8 % compared to the CFD results. An empirical relationship for the area-weighted average shear stress was developed for water and activated sludge...

In this paper the bubble issuing from an orifice at the bottom of the boundary evolution in a finite Non-Newtonianfluid(such as Maxwell fluid,Carreu fluid)is numerically simulated The effects of the rheological behavior,physical parameters and circumstantial conditions are discussed in detail

We employ a weakly nonlinear perturbative scheme to investigate the stretch flow of a non-Newtonianfluid confined in Hele-Shaw cell for which the upper plate is lifted. A generalized Darcy's law is utilized to model interfacial fingering formation in both the weak shear-thinning and weak shear-thickening limits. Within this context, we analyze how the interfacial finger shapes and the nonlinear competition dynamics among fingers are affected by the non-Newtonian nature of the stretched fluid.

We describe a simple, low-cost experiment and corresponding pedagogical strategies for studying fluids whose viscosities depend on shear rate, referred to as "non-Newtonianfluids." We developed these materials teaching for the Compass Project, an organization that fosters a creative, diverse, and collaborative community of science…

In this series of articles, the authors discuss various phenomenain fluid dynamics, which may be investigated via tabletopexperiments using low-cost or home-made instruments.The fifth article in this series is about some fascinating experimentswith non-Newtonianfluids.

Describes an experimental program to examine flow curve determination for non-Newtonianfluids. Includes apparatus used (a modification of Walawender and Chen's set-up, but using a 50cc buret connected to a glass capillary through a Tygon tube), theoretical information, procedures, and typical results obtained. (JN)

Non-Newtonianfluid mechanics is a vast subject that has several journals partly, or primarily, dedicated to its investigation (Journal of Non-NewtonianFluid Mechanics, Rheologica Acta, Journal of Fluid Mechanics, Journal of Rheology, amongst others). It is an area of active research, both for industrial fluid problems and for applications elsewhere, notably geophysically motivated issues such as the flow of lava and ice, mud slides, snow avalanches and debris flows. The main motivati on for this research activity is that, apart from some annoyingly common fluids such as air and water, virtually no fluid is actually Newtonian (that is, having a simple linear relation between stress and strain-rate characterized by a constant viscosity). Several textbooks are useful sources of information; for example, [1-3] are standard texts giving mathematical and engineering perspectives upon the subject. In these lecture notes, Ancey's chapter on rheology (Chap. 3) gives further introduction.

The rheology and molecular structure of a model bitumen (Cooee bitumen) under shear are investigated in the non-Newtonian regime using non-equilibrium molecular dynamics simulations. The shear viscosity, normal stress differences, and pressure of the bitumen mixture are computed at different shear...... rates and different temperatures. The model bitumen is shown to be a shear-thinning fluid at all temperatures. In addition, the Cooee model is able to reproduce experimental results showing the formation of nanoaggregates composed of stacks of flat aromatic molecules in bitumen. These nanoaggregates...

for optimizing MBR-systems is computational fluid dynamics (CFD) modelling, giving the ability to describe the flow in the systems. A parameter which is often neglected in such models is the non-Newtonian properties of active sludge, which is of great importance for MBR systems since they operate at sludge...... concentrations up to a factor 10 compared to conventional activated sludge (CAS) systems, resulting in strongly shear thinning liquids. A CFD-model is validated against measurements conducted in a system with rotating cross flow membranes submerged in non-Newtonian liquids, where tangential velocities...

Progress of technology and medicine dictates the ever-increasing requirements (heat resistance, corrosion resistance, strength properties, impregnating ability, etc.) for non-Newtonianfluids and materials produced on their basis (epoxy resin, coating materials, liquid crystals, etc.). Materials with improved properties obtaining is possible by modification of their physicochemical structure. One of the most promising approaches to the restructuring of non-Newtonianfluids is cavitation generated by high-frequency acoustic vibrations. The efficiency of cavitation in non-Newtonianfluid is determined by dynamics of gaseous bubble. Today, bubble dynamics in isotropic non-Newtonianfluids, in which cavitation bubble shape remains spherical, is most full investigated, because the problem reduces to ordinary differential equation for spherical bubble radius. However, gaseous bubble in anisotropic fluids which are most wide kind of non-Newtonianfluids (due to orientation of macromolecules) deviates from spherical shape due to viscosity dependence on shear rate direction. Therefore, the paper presents the mathematical model of gaseous bubble dynamics in anisotropic non-Newtonianfluids. The model is based on general equations for anisotropic non-Newtonianfluid flow. The equations are solved by asymptotic decomposition of fluid flow parameters. It allowed evaluating bubble size and shape evolution depending on rheological properties of liquid and acoustic field characteristics.

Full Text Available The aim of this work is related to an analysis of journal bearings lubrication using non-Newtonianfluids which are described by a power-law model. The performance characteristics of the journal bearings are determined for various values of the non-Newtonian power-law index “” which is equal to: 0.9, 1, and 1.1. Obtained numerical results show that for the dilatant fluids (, the load-carrying capacity, the pressure, the temperature, and the frictional force increased while for the pseudo-plastic fluids ( they decreased. The influence of the thermal effects on these characteristics is important at higher values of the flow behavior index “.” Obtained results are compared to those obtained by others. Good agreement is observed between the different results.

Three tests on non-Newtonianfluids were used to verify the use of a vertically rotating flume (VRF) for the study of the rheological properties of debris flow. The VRF is described and a procedure for the analysis of results of tests made with the VRF is presented. The major advantages of the VRF are a flow field consistent with that found in nature, a large particle-diameter threshold, inexpensive operation, and verification using several different materials; the major limitations are a lack of temperature control and a certain error incurred from the use of the Bingham plastic model to describe a more complex phenomenon. Because the VRF has been verified with non-Newtonianfluids as well as Newtonian fluids, it can be used to measure the rheological properties of coarse-grained debris-flow materials.

A binary equimolar dense fluid mixture is subjected to a shear. The orientational distribution of particles of type i around particles of type j (i, j = 1, 2) and the distortion of the radial distribution function is discussed for planar Couette flow. Results are presented in terms of a mixture of soft spheres, for which one species differs substantially in size and mass from the other, simulated on the computer using the technique of shear nonequilbrium molecular dynamics. Transport coefficients, including those associated with normal pressure differences, are given for the mixture and for the species in the mixture. Non-Newtonian phenomena are observed.

Full Text Available Steady two-dimensional natural convection in fluid filled cavities is numerically investigated for the case of non-
Newtonianshear thickening power law liquids. The conservation equations of mass, momentum and energy under the
assumption of a Newtonian Boussinesq fluid have been solved using the finite volume method for Newtonian and
non-Newtonianfluids. The computations were performed for a Rayleigh number, based on cavity height, of 105 and a
Prandtl number of 100. In all of the numerical experiments, the channel is heated from below and cooled from the top
with insulated side-walls and the inclination angle is varied. The simulations have been carried out for aspect ratios of
1 and 4. Comparison between the Newtonian and the non-Newtonian cases is conducted based on the dependence of
the average Nusselt number on angle of inclination. It is shown that despite significant variation in heat transfer rate
both Newtonian and non-Newtonianfluids exhibit similar behavior with the transition from multi-cell flow structure
to a single-cell regime.

Electrokinetically driven microfluidic devices are usually used to analyze and process biofluids which can be classified as non-Newtonianfluids. Conventional electrokinetic theories resulting from Newtonian hydrodynamics then fail to describe the behaviors of these fluids. In this study, a theoretical analysis of electro-osmotic mobility of non-Newtonianfluids is reported. The general Cauchy momentum equation is simplified by incorporation of the Gouy-Chapman solution to the Poisson-Boltzmann equation and the Carreau fluid constitutive model. Then a nonlinear ordinary differential equation governing the electro-osmotic velocity of Carreau fluids is obtained and solved numerically. The effects of the Weissenberg number (Wi), the surface zeta potential (ψ¯s), the power-law exponent(n), and the transitional parameter (β) on electro-osmotic mobility are examined. It is shown that the results presented in this study for the electro-osmotic mobility of Carreau fluids are quite general so that the electro-osmotic mobility for the Newtonian fluids and the power-law fluids can be obtained as two limiting cases.

We discuss the roles of viscosity in relativistic fluid dynamics from the point of view of memory effects. Depending on the type of quantity to which the memory effect is applied, different terms appear in higher order corrections. We show that when the memory effect applies on the extensive quantities, the hydrodynamic equations of motion become non-singular. We further discuss the question of memory effect in the derivation of transport coefficients from a microscopic theory. We generalize the application of the Green-Kubo-Nakano (GKN) to calculate transport coefficients in the framework of projection operator formalism, and derive the general formula when the fluid is non-Newtonian.

The global static stability of a Starling Resistor conveying non-Newtonianfluid is considered. The Starling Resistor consists of two rigid circular tubes and axisymmetric collapsible tube mounted between them. Upstream and downstream pressures are the boundary condition as well as external to the collapsible tube pressure. Quasi one-dimensional model has been proposed and a boundary value problem in terms of nondimensional parameters obtained. Nonuniqueness of the boundary value problem is regarded as static instability. The analytical condition of instability which defines a surface in parameter space has been studied numerically. The influence of fluid rheology on stability of collapsible tube is established.

The present paper investigates the asymptotic behavior of solutions for stochastic non-Newtonianfluids in a two-dimensional domain.Firstly,we prove the existence of random attractors AH(ω) in H; Secondly,we prove the existence of random attractors Av(ω) in V.Then we verify regularity of the random attractors by showing that AH(ω) =Av(ω),which implies the smoothing effect of the fluids in the sense that solution becomes eventually more regular than the initial data.

The in situ rheology of polymeric solutions has been studied experimentally in etched silicon micromodels which are idealizations of porous media. The rectangular channels in these etched networks have dimensions typical of pore sizes in sandstone rocks. Pressure drop/flow rate relations have been measured for water and non-Newtonian hydrolyzed-polyacrylamide (HPAM) solutions in both individual straight rectangular capillaries and in networks of such capillaries. Results from these experiments have been analyzed using pore-scale network modeling incorporating the non-Newtonianfluid mechanics of a Carreau fluid. Quantitative agreement is seen between the experiments and the network calculations in the Newtonian and shear-thinning flow regions demonstrating that the 'shift factor,'alpha, can be calculated a priori. Shear-thickening behavior was observed at higher flow rates in the micromodel experiments as a result of elastic effects becoming important and this remains to be incorporated in the network model.

We present a theoretical analysis for heat transfer in power law non-Newtonianfluid by assuming that the thermal diffusivity is a function of temperature gradient. The laminar boundary layer energy equation is considered as an example to illustrate the application. It is shown that the boundary layer energy equation subject to the corresponding boundary conditions can be transformed to a boundary value problem of a nonlinear ordinary differential equation when similarity variables are introduced. Numerical solutions of the similarity energy equation are presented.

Finite-amplitude thermal convection in a shear-thinning fluid layer between two horizontal plates of finite thermal conductivity is considered. Weakly nonlinear analysis is adopted as a first approach to investigate nonlinear effects. The rheological behavior of the fluid is described by the Carreau model. As a first step, the critical conditions for the onset of convection are computed as a function of the ratio ξ of the thermal conductivity of the plates to the thermal conductivity of the fluid. In agreement with the literature, the critical Rayleigh number Ra(c) and the critical wave number k(c) decrease from 1708 to 720 and from 3.11 to 0, when ξ decreases from infinity to zero. In the second step, the critical value α(c) of the shear-thinning degree above which the bifurcation becomes subcritical is determined. It is shown that α(c) increases with decreasing ξ. The stability of rolls and squares is then investigated as a function of ξ and the rheological parameters. The limit value ξ(c), below which squares are stable, decreases with increasing shear-thinning effects. This is related to the fact that shear-thinning effects increase the nonlinear interactions between sets of rolls that constitute the square patterns [M. Bouteraa et al., J. Fluid Mech. 767, 696 (2015)]. For a significant deviation from the critical conditions, nonlinear convection terms and nonlinear viscous terms become stronger, leading to a further diminution of ξ(c). The dependency of the heat transfer on ξ and the rheological parameters is reported. It is consistent with the maximum heat transfer principle. Finally, the flow structure and the viscosity field are represented for weakly and highly conducting plates.

We report an experimental study of the intermittent dynamics of a gas flowing through a column of a non-Newtonianfluid. In a given range of the imposed constant flow rate, the system spontaneously alternates between two regimes: bubbles emitted at the bottom either rise independently one from the other or merge to create a winding flue which then connects the bottom air entrance to the free surface. The observations are reminiscent of the spontaneous changes in the degassing regime observed on volcanoes and suggest that, in the nature, such a phenomenon is likely to be governed by the non-Newtonian properties of the magma. We focus on the statistical distribution of the lifespans of the bubbling and flue regimes in the intermittent steady state. The bubbling regime exhibits a characteristic time whereas, interestingly, the flue lifespan displays a decaying power-law distribution. The associated exponent, which is significantly smaller than the value 1.5 often reported experimentally and predicted in some standard intermittency scenarios, depends on the fluid properties and can be interpreted as the ratio of two characteristic times of the system.

A procedure is outlined for the numerical solution of the complete elastohydrodynamic lubrication of rectangular contacts incorporating a non-Newtonianfluid model. The approach uses a Newtonian model as long as the shear stress is less than a limiting shear stress. If the shear stress exceeds the limiting value, the shear stress is set equal to the limiting value. The numerical solution requires the coupled solution of the pressure, film shape, and fluid rheology equations from the inlet to the outlet. Isothermal and no-side-leakage assumptions were imposed in the analysis. The influence of dimensionless speed, load, materials, and sliding velocity and limiting-shear-strength proportionality constant on dimensionless minimum film thickness was investigated. Fourteen cases were used in obtaining the minimum-film-thickness equation for an elastohydrodynamically lubricated rectangular contact incorporating a non-Newtonianfluid model. Computer plots are also presented that indicate in detail pressure distribution, film shape, shear stress at the surfaces, and flow throughout the conjunction.

Full Text Available The objective of this work is to study the effect of confining walls on the free settling of spherical particles along the axes of five vertical cylindrical tubes in Newtonian and non-Newtonian liquids. Experimental results were predominantly obtained in the particle flow region between the Stokes and the Newton regimes (intermediate region and displayed Reynolds numbers in the ranges 0.7shear rate of spheres in non-Newtonianfluids.

We describe a simple, low-cost experiment and corresponding pedagogical strategies for studying fluids whose viscosities depend on shear rate, referred to as non-Newtonianfluids. We developed these materials teaching for the Compass Project, an organization that fosters a creative, diverse, and collaborative community of science students at UC Berkeley. Incoming freshmen worked together in a week-long, residential program to explore physical phenomena through a combination of conceptual model-building and hands-on experimentation. During the program, students were exposed to three major aspects of scientific discovery: developing a model, testing the model, and investigating deviations from the model.

Systems involving the flow of non-Newtonianfluids in porous media arise in a number of settings, including hydraulic fracturing, enhanced oil recovery, contaminant remediation, and biological systems. Development of accurate macroscale models of such systems requires an understanding of the relationship between the fluid and medium properties at the microscale and averaged macroscale properties. This study investigates the flow of aqueous solutions of guar gum, a major component of hydraulic fracturing fluids that exhibits Cross model rheological behavior. The rheological properties of solutions containing varying concentrations of guar gum were characterized using a rotational rheometer and the data were fit to a model relating viscosity to shear rate and concentration. Flow experiments were conducted in a porous medium-packed column to measure the pressure response during the flow of guar gum solutions at a wide range of flow rates and determine apparent macroscale viscosities and shear rates. To investigate the relationship between the fluid rheology, microscale physics, and the observed macroscale properties, a lattice Boltzmann pore scale simulator incorporating non-Newtonian behavior was developed. The model was validated, then used to simulate systems representative of the column experiments, allowing direct correlation of detailed microscale physics to the macroscale observations.

Four commonly used refractive-index (RI)-matched Newtonian blood-analog fluids are reviewed, and different non-Newtonian blood-analogs, with RI of 1.372-1.495, are investigated. Sodium iodide (NaI), sodium thiocyanate (NaSCN) and potassium thiocyanate are used to adjust the RI of blood-analogs to that of test sections for minimizing optical distortions in particle image velocimetry data, and xanthan gum (XG) is added to the fluids to give them non-Newtonian properties (shear thinning and viscoelasticity). Our results support the general belief that adding NaI to Newtonian fluids matches the RI without changing the kinematic viscosity. However, in contrast to claims made in a few studies that did not measure rheology, our investigation revealed that adding NaI or NaSCN to XG-based non-Newtonianfluids changes the viscosity of the fluids considerably and reduces the shear-thinning property. Therefore, the RI of non-Newtonian blood-analog fluids with XG cannot be adjusted easily by varying the concentration of NaI or NaSCN and needs more careful rheological study.

This paper presents a method for calculating the wall shear rate in pipe turbulent flow. It collapses adequately the data measured in laminar flow and turbulent flow into a single flow curve and gives the basis for the design of turbulent flow viscometers. Key words: non-Newtonian, wall shear rate, turbulent, rheometer

One of the goals of this program was to develop the experimental and analytical/computational tools required to predict the flow of non-Newtonianfluids through the various system components of a propulsion system: pipes, valves, pumps etc. To achieve this goal we selected to augment the capabilities of NASA's Generalized Fluid System Simulation Program (GFSSP) software. GFSSP is a general-purpose computer program designed to calculate steady state and transient pressure and flow distributions in a complex fluid network. While the current version of the GFSSP code is able to handle various systems components the implicit assumption in the code is that the fluids in the system are Newtonian. To extend the capability of the code to non-Newtonianfluids, such as silica gelled fuels and oxidizers, modifications to the momentum equations of the code have been performed. We have successfully implemented in GFSSP flow equations for fluids with power law behavior. The implementation of the power law fluid behavior into the GFSSP code depends on knowledge of the two fluid coefficients, n and K. The determination of these parameters for the silica gels used in this program was performed experimentally. The n and K parameters for silica water gels were determined experimentally at CFDRC's Special Projects Laboratory, with a constant shear rate capillary viscometer. Batches of 8:1 (by weight) water-silica gel were mixed using CFDRC s 10-gallon gelled propellant mixer. Prior to testing the gel was allowed to rest in the rheometer tank for at least twelve hours to ensure that the delicate structure of the gel had sufficient time to reform. During the tests silica gel was pressure fed and discharged through stainless steel pipes ranging from 1", to 36", in length and three diameters; 0.0237", 0.032", and 0.047". The data collected in these tests included pressure at tube entrance and volumetric flowrate. From these data the uncorrected shear rate, shear stress, residence time

The analyses of the effects of non-Newtonian viscosity on the membrane of red blood cells (RBCs) suspended in a shear flow are presented. The specific objective is to investigate the mechanical deformation on the surfaces of an ellipsoidal particle model. The hydrodynamic stresses and other forces on the surface of the particle are used to determine the cell deformation. We extended previous works, which were based on the Newtonian fluid models, to the non-Newtonian case, and focus on imposed shear rate values between 1 and 100 per second. Two viscosity models are investigated, which respectively correspond to a normal person and a patient with cerebrovascular accident (CVA). The results are compared with those obtained assuming a Newtonian model. We observed that the orientation of the cell influences the deformation and the imposed shear rate drives the local shear rate distribution along the particle surface. The integral particle deformation for the non-Newtonian models in the given shear rate regime is higher than that for the Newtonian reference model. Finally, the deformation of the cell surface decreases as the dissipation ratio increases.

Spreading non-Newtonian liquids with non-power-law rheology on completely wetting surfaces are seldom investigated. This study assessed the wetting behavior of polydimethylsiloxane (PDMS), a Newtonian fluid, two carboxymethylcellulose (CMC) sodium solutions, a PDMS+2%w/w silica nanoparticle suspension and three polyethylene glycol (PEG400)+5-10%w/w silica nanoparticle suspensions (non-power-law fluids) on a mica surface. The theta(D)-U and R-t data for spreading drops of the six tested, non-power-law fluids can be described by power-law wetting models. We propose that this behavior is attributable to a uniform shear rate (a few tens to a few hundreds of s(-1)) distributed over the thin-film regime that controls spreading dynamics. Estimated film thickness was below the resolution of an optical microscope for direct observation. Approximating a general non-Newtonianfluid spreading as a power-law fluid greatly simplifies theoretical analysis and data interpretation.

This paper is joint with [27].The authors prove in this article the existence and reveal its structure of uniform attractor for a two-dimensional nonautonomous incompressible non-Newtonianfluid with a new class of external forces.

Full Text Available This paper investigates the limiting behavior of attractors for a two-dimensional incompressible non-Newtonianfluid under small random perturbations. Under certain conditions, the upper semicontinuity of the attractors for diminishing perturbations is shown.

The rheology and molecular structure of a model bitumen (Cooee bitumen) under shear is investigated in the non-Newtonian regime using non-equilibrium molecular dynamics simulations. The shear viscosity and normal stress differences of the bitumen mixture are computed at different shear rates and different temperatures. The model bitumen is shown to be a shear-thinning fluid. The corresponding molecular structure is studied at the same shear rates and temperatures. The Cooee bitumen is able to reproduce experimental results showing the formation of nanoaggregates composed of stacks of flat aromatic molecules. These nanoaggregates are immersed in a solvent of saturated hydrocarbon molecules. The nanoaggregates are shown to break up at very high shear rates, leading only to a minor effect on the viscosity of the mixture. At low shear rates, bitumen can be seen as a colloidal suspension of nanoaggregates in a solvent. The slight anisotropy of the whole sample due to the nanoaggregates is considered and quantified...

The paper focuses on the data collected from the mixing of shear thinning non-Newtonianfluids in a cylindrical tank by a Rushton turbine. The data presented are obtained by using Computational Fluid Dynamics (CFD) simulation of fluid flow field in the entire tank volume. The CFD validation data for this study is reported in the research article 'Numerical investigation of hydrodynamic behavior of shear thinning fluids in stirred tank' (Khapre and Munshi, 2015) [1]. The tracer injection method is used for the prediction of mixing time and mixing efficiency of a Rushton turbine impeller.

Full Text Available The paper focuses on the data collected from the mixing of shear thinning non-Newtonianfluids in a cylindrical tank by a Rushton turbine. The data presented are obtained by using Computational Fluid Dynamics (CFD simulation of fluid flow field in the entire tank volume. The CFD validation data for this study is reported in the research article ‘Numerical investigation of hydrodynamic behavior of shear thinning fluids in stirred tank’ (Khapre and Munshi, 2015 [1]. The tracer injection method is used for the prediction of mixing time and mixing efficiency of a Rushton turbine impeller.

The experimental research on the non-Newtonian flow characteristic of a waxy crude oil was conducted through a rotational parallel-plates rheometer system.The test temperature is about 6.5 ℃ higher than its gel point.The shear stress and viscosity of the waxy crude oil show sophisticate non-Newtonian characteristics in the shear rate of 10-4-102 s-1,in which the shear stress can be divided into three parts qualitatively,i.e.stress-up region,leveling-off region,and stress-up region.This indicates that there is a yielding process in shearing for the waxy crude oil at the experimental temperature,which is similar to the yield phenomenon in thixotropy-loop test discussed by CHANG and BOGER.Furthermore,the steady shear experiment after the pre-shear process shows that the stress leveling-off region at low shear rate disappears for the waxy crude oil and the stress curve becomes a monotonic climbing one,which demonstrates that the internal structure property presenting through yielding stress at low shear rate can be changed by shearing.The experimental results also show that the internal structure of waxy crude oil presenting at low shear rate has no influence on the shear viscosity obtained at the shear rate higher than 0.1 s-1.The generalized Newtonian model is adopted to describe the shear-thinning viscosity property of the waxy crude oil at high shear rate.

Full Text Available Dampers are widely applied to protect devices or human body from severe impact or harmful vibration circumstances. Considering that dampers with low velocity exponent have advantages in energy absorption, they have been widely used in antiseismic structures and shock buffering. Non-Newtonianfluid with strong shear-thinning effect is commonly adopted to achieve this goal. To obtain the damping mechanism and find convenient methods to design the nonlinear fluid damper, in this study, a hydraulic damper is filled with 500,000 cSt silicone oil to achieve a low velocity exponent. Drop hammer test is carried out to experimentally obtain its impact and buffering characteristics. Then a coupling model is built to analyze its damping mechanism, which consists of a model of impact system and a computational fluid dynamics (CFD model. Results from the coupling model can be consistent with the experiment results. Simulation method can help design non-Newtonianfluid dampers more effectively.

Full Text Available This article concerns systems of equations that model incompressible bipolar non-Newtonianfluid motion in the whole space $mathbb{R}^n$. Using the improved Fourier splitting method, we prove that a weak solution decays in the $L^2$ norm at the same rate as $(1+t^{-n/4}$ as the time $t$ approaches infinity. Also we obtain optimal $L^2$ error-estimates for Newtonian and Non-Newtonian flows.

Membrane bioreactor (MBR) systems are often considered as the wastewater treatment method of the future due to their high effluent quality. One of the main problems with such systems is a relative large energy consumption, compared to conventional activated sludge (CAS) systems, which has led to further research in this specific area. A powerful tool for optimizing MBR-systems is computational fluid dynamics (CFD) modelling, which gives researchers the ability to describe the flow in the systems. A parameter which is often neglected in such models is the non-Newtonian properties of active sludge, which is of great importance for MBR systems since they operate at sludge concentrations up to a factor of 10 compared to CAS systems, resulting in strongly shear thinning liquids. A CFD-model is validated against measurements conducted in a system with rotating cross-flow membranes submerged in non-Newtonian liquids, where tangential velocities are measured with a Laser Doppler Anemometer (LDA). The CFD model is found to be capable of modelling the correct velocities in a range of setups, making CFD models a powerful tool for optimization of MBR systems.

To predict correctly the castings process of self compacting concrete a numerical model capable of simulating flow patterns at the structural scale and at the same time the impact of the varying volume fraction of aggregates and other phenomena at the scale of aggregates on the flow evolution...... is necessary. In this contribution, the model at the scale of aggregates is introduced. The conventional lattice Boltzmann method for fluid flow is enriched with the immersed boundary method with direct forcing to simulate the flow of rigid particles in a non- Newtonian liquid. Basic ingredients of the model...... are presented and discussed with the emphasis on a newly developed algorithm for the dynamics of particles whose interactions strongly depend on velocities of particles. The application of the model is demonstrated by a parametric study with varying volume fractions of aggregates and speed of shearing used...

Classic porous media characterization relies on typical infiltration experiments with Newtonian fluids (i.e., water) to estimate hydraulic conductivity. However, such experiments are generally not able to discern important characteristics such as pore size distribution or pore structure. We show that introducing non-Newtonianfluids provides additional unique flow signatures that can be used for improved pore structure characterization while still representing the functional hydraulic behavior of real porous media. We present a new method for experimentally estimating the pore structure of porous media using a combination of Newtonian and non-Newtonianfluids. The proposed method transforms results of N infiltration experiments using water and N-1 non-Newtonian solutions into a system of equations that yields N representative radii (Ri) and their corresponding percent contribution to flow (wi). This method allows for estimating the soil retention curve using only saturated experiments. Experimental and numerical validation comparing the functional flow behavior of different soils to their modeled flow with N representative radii revealed the ability of the proposed method to represent the water retention and infiltration behavior of real soils. The experimental results showed the ability of such fluids to outsmart Newtonian fluids and infer pore size distribution and unsaturated behavior using simple saturated experiments. Specifically, we demonstrate using synthetic porous media that the use of different non-Newtonianfluids enables the definition of the radii and corresponding percent contribution to flow of multiple representative pores, thus improving the ability of pore-scale models to mimic the functional behavior of real porous media in terms of flow and porosity. The results advance the knowledge towards conceptualizing the complexity of porous media and can potentially impact applications in fields like irrigation efficiencies, vadose zone hydrology, soil

An analysis of nonlinear transverse shear wave has been carried out on non-Newtonian viscoelastic liquid using generalized hydrodynamic model. The nonlinear viscoelastic behavior is introduced through velocity shear dependence of viscosity coefficient by well known Carreau-Bird model. The dynamical feature of this shear wave leads to the celebrated Fermi-Pasta-Ulam problem. Numerical solution has been obtained which shows that initial periodic solutions reoccur after passing through several patterns of periodic waves. A possible explanation for this periodic solution is given by constructing modified Korteweg de Vries equation. This model has application from laboratory to astrophysical plasmas as well as in biological systems.

An analysis of nonlinear transverse shear wave has been carried out on non-Newtonian viscoelastic liquid using generalized hydrodynamic(GH) model. The nonlinear viscoelastic behavior is introduced through velocity shear dependence of viscosity coefficient by well known Carreau -Bird model. The dynamical feature of this shear wave leads to the celebrated Fermi-Pasta-Ulam (FPU) problem. Numerical solution has been obtained which shows that initial periodic solutions reoccur after passing through several patterns of periodic waves. A possible explanation for this periodic solution is given by constructing modified Korteweg de Vries (mKdV) equation. This model has application from laboratory to astrophysical plasmas as well as biological systems.

Electro-osmosis in porous media has many important applications in various areas such as oil and gas exploitation and biomedical detection. Very often, fluids relevant to these applications are non-Newtonian because of the shear-rate dependent viscosity. The purpose of this study was to investigate the behaviors and physical mechanism of electro-osmosis of non-Newtonianfluids in porous media. Model porous microstructures (granular, fibrous, and network) were created by a random generation-growth method. The nonlinear governing equations of electro-kinetic transport for a power-law fluid were solved by the lattice Poisson-Boltzmann method (LPBM). The model results indicate that: (i) the electro-osmosis of non-Newtonianfluids exhibits distinct nonlinear behaviors compared to that of Newtonian fluids; (ii) when the bulk ion concentration or zeta potential is high enough, shear-thinning fluids exhibit higher electro-osmotic permeability, while shear-thickening fluids lead to the higher electro-osmotic permeability for very low bulk ion concentration or zeta potential; (iii) the effect of the porous medium structure depends significantly on the constitutive parameters: for fluids with large constitutive coefficients strongly dependent on the power-law index, the network structure shows the highest electro-osmotic permeability while the granular structure exhibits the lowest permeability on the entire range of power law indices considered; when the dependence of the constitutive coefficient on the power law index is weaker, different behaviors can be observed especially in case of strong shear thinning.

We study four non-Newtonianfluid mechanics problems using Mathematica[R]. Constitutive equations describing the behavior of power-law, Bingham and Carreau models are recalled. The velocity profile is obtained for the horizontal flow of power-law fluids in pipes and annuli. For the vertical laminar film flow of a Bingham fluid we determine the…

We study four non-Newtonianfluid mechanics problems using Mathematica[R]. Constitutive equations describing the behavior of power-law, Bingham and Carreau models are recalled. The velocity profile is obtained for the horizontal flow of power-law fluids in pipes and annuli. For the vertical laminar film flow of a Bingham fluid we determine the…

In this paper the flow near a two-dimensional stagnation point for a particular non-Newtonianfluid has been studied. Non-Newtonianfluids form a wide class of different materials, which will be used very often in chemical industries. From a practical point of view it is of great importance to obtain some results for example concerning the flow rate and the losses in a tube, the drag and the separation point of a boundary layer flow etc. for such fluids. Therefore it is necessary to assume a particular constitutive equation to calculate various aspects. (author)

Flow of generalized Newtonian fluids in porous media can be modeled as a bundle of capillary tubes or a pore-scale network. In general, both approaches rely on the solution of Hagen–Poiseuille equation using power law to estimate the variations in the fluid viscosity due to the applied shear rate. Despite the effectiveness and simplicity, power law tends to provide unrealistic values for the effective viscosity especially in the limits of zero and infinite shear rates. Here, instead of using power law, Carreau model (bubbles, drops, and particles in non-Newtonianfluids. Taylor & Francis Group, New York, 2007) is used to determine the effective viscosity as a function of the shear strain rate. Carreau model can predict accurately the variation in the viscosity at all shear rates and provide more accurate solution for the flow physics in a single pore. Using the results for a single pore, normalized Fanning friction coefficient has been calculated and plotted as a function of the newly defined Reynolds number based on pressure gradient. For laminar flow, the variation in the friction coefficient with Reynolds number has been plotted and scaled. It is observed that generalized Newtonian fluid flows show Newtonian nature up to a certain Reynolds number. At high Reynolds number, deviation from the Newtonian behavior is observed. The main contribution of this paper is to present a closed-form solution for the flow in a single pore using Carreau model, which allows for fast evaluation of the relationship between flux and pressure gradient in an arbitrary pore diameter. In this way, we believe that our development will open the perspectives for using Carreau models in pore-network simulations at low computational costs to obtain more accurate prediction for generalized Newtonian fluid flows in porous media.

A numerical framework capable of predicting the free surface flow of a suspension of rigid particles in a non-Newtonianfluid is described. The framework is a combination of the lattice Boltzmann method for fluid flow, the mass tracking algorithm for free surface representation, the immersed...

This article illustrates how a computer algebra system, such as Maple[R], can assist in the study of theoretical fluid mechanics, for both Newtonian and non-Newtonianfluids. The continuity equation, the stress equations of motion, the Navier-Stokes equations, and various constitutive equations are treated, using a full, but straightforward,…

The swimming process by which mammal spermatozoa progress towards an egg within the reproductive organs is important in achieving successful internal fertilization. The viscosity of oviductal mucus is more than two orders of magnitude greater than that of water, and oviductal mucus also has non-Newtonian properties. In this study, we experimentally observed sperm motion in fluids with various fluid rheological properties and investigated the influence of varying the viscosity and whether the fluid was Newtonian or non-Newtonian on the sperm motility. We selected polyvinylpyrrolidone and methylcellulose as solutes to create solutions with different rheological properties. We used the semen of Japanese cattle and investigated the following parameters: the sperm velocity, the straight-line velocity and the amplitude from the trajectory, and the beat frequency from the fragellar movement. In a Newtonian fluid environment, as the viscosity increased, the motility of the sperm decreased. However, in a non-Newtonianfluid, the straight-line velocity and beat frequency were significantly higher than in a Newtonian fluid with comparable viscosity. As a result, the linearity of the sperm movement increased. Additionally, increasing the viscosity brought about large changes in the sperm flagellar shape. At low viscosities, the entire flagellum moved in a curved flapping motion, whereas in the high-viscosity, only the tip of the flagellum flapped. These results suggest that the bovine sperm has evolved to swim toward the egg as quickly as possible in the actual oviduct fluid, which is a high-viscosity non-Newtonianfluid.

This article illustrates how a computer algebra system, such as Maple[R], can assist in the study of theoretical fluid mechanics, for both Newtonian and non-Newtonianfluids. The continuity equation, the stress equations of motion, the Navier-Stokes equations, and various constitutive equations are treated, using a full, but straightforward,…

As part of a project to develop an integrated microfluidic biosensor for the detection of small molecules in saliva, practical issues of extraction of analytes from non-Newtonian samples using an H-filter were explored. The H-filter can be used to rapidly and efficiently extract small molecules from a complex sample into a simpler buffer. The location of the interface between the sample and buffer streams is a critical parameter in the function of the H-filter, so fluorescence microscopy was employed to monitor the interface position; this revealed apparently anomalous fluorophore diffusion from the samples into the buffer solutions. Using confocal microscopy to understand the three-dimensional distribution of the fluorophore, it was found that the interface between the non-Newtonian sample and Newtonian buffer was both curved and unstable. The core of the non-Newtonian sample extended into the Newtonian buffer and its position was unstable, producing a fluorescence intensity profile that gave rise to the apparently anomalously fast fluorophore transport. These instabilities resulted from the pairing of rheologically dissimilar fluid streams and were flowrate dependent. We conclude that use of non-Newtonianfluids, such as saliva, in the H-filter necessitates pretreatment to reduce viscoelasticity. The interfacial variation in position, stability and shape caused by the non-Newtonian samples has substantial implications for the use of biological samples for quantitative analysis and analyte extraction in concurrent flow extraction devices.

Fluids present or used in biology, medicine and (biomedical) engineering are often significantly non-Newtonian. Furthermore, they are chemically complex and can interact with the porous matrix through which they flow. The porous structures themselves display complex morphological inhomogeneities on a wide range of length scales. In vertebroplasty, a shear-thinning fluid, e.g. poly(methyl methacrylate) (PMMA), is injected into the cavities of vertebral trabecular bone for the stabilization of fractures and metastatic lesions. The main objective of this study was therefore to provide a protocol for numerically investigating the rheological properties of PMMA-based bone cements to predict its spreading behavior while flowing through vertebral trabecular bone. A numerical upscaling scheme based on a dimensionless formulation of the Navier-Stokes equation is proposed in order to relate the pore-scale rheological properties of the PMMA that were experimentally estimated using a plate rheometer, to the continuum-scale. On the pore length scale, a viscosity change on the order of one magnitude was observed whilst the shear-thinning properties caused a viscosity change on the order of only 10% on the continuum length scale and in a flow regime that is relevant for vertebroplasty. An experimental validation, performed on human cadaveric vertebrae (n=9), showed a significant improvement of the cement spreading prediction accuracy with a non-Newtonian formulation. A root mean square cement surface prediction error of 1.53mm (assuming a Newtonian fluid) and 1.37mm (assuming a shear-thinning fluid) was found. Our findings highlight the importance of incorporating the non-Newtonianfluids properties in computational models of porous media at the appropriate length scale.

Classic porous media characterization relies on typical infiltration experiments with Newtonian fluids (i.e., water) to estimate hydraulic conductivity. However, such experiments are generally not able to discern important characteristics such as pore size distribution or pore structure. We show that introducing non-Newtonianfluids provides additional unique flow signatures that can be used for improved pore structure characterization. We present a new method that transforms results of N infiltration experiments using water and N-1 non-Newtonian solutions into a system of equations that yields N representative radii (Ri) and their corresponding percent contribution to flow (wi). Those radii and weights are optimized in terms of flow and porosity to represent the functional hydraulic behavior of real porous media. The method also allows for estimating the soil retention curve using only saturated experiments. Experimental and numerical validation revealed the ability of the proposed method to represent the water retention and functional infiltration behavior of real soils. The experimental results showed the ability of such fluids to outsmart Newtonian fluids and infer pore size distribution and unsaturated behavior using simple saturated experiments. Specifically, we demonstrate using synthetic porous media composed of different combinations of sizes and numbers of capillary tubes that the use of different non-Newtonianfluids enables the prediction of the pore structure. The results advance the knowledge towards conceptualizing the complexity of porous media and can potentially impact applications in fields like irrigation efficiencies, vadose zone hydrology, soil-root-plant continuum, carbon sequestration into geologic formations, soil remediation, petroleum reservoir engineering, oil exploration and groundwater modeling.

Holography made possible the analysis of drop formation in Newtonian and non-Newtonianfluids. The drops were illuminated at the moment of their formation with an impulse ruby laser, and from the holograms the whole spray was reconstructed with a closed-circuit TV loop. From the pictures taken from different planes of the spray, the size and the spatial distribution of the drops were determined with an electrooptical analyzer. The holographic measuring method provided quantitative data phenomena which were qualitatively observable on high-speed films. The experiments also verified an equation involving dimensionless criteria, deduced fo the atomization of non-Newtonian substances.

This article proves that the random dynamical system generated by a two- dimensional incompressible non-Newtonianfluid with multiplicative noise has a global random attractor, which is a random compact set absorbing any bounded nonrandom subset of the phase space.

is necessary. In this contribution, the model at the scale of aggregates is introduced. The conventional lattice Boltzmann method for fluid flow is enriched with the immersed boundary method with direct forcing to simulate the flow of rigid particles in a non- Newtonian liquid. Basic ingredients of the model...

Quantification of mass transfer in porous microchannel is of paramount importance in several applications. Transport of neutral solute in presence of convective-diffusive EOF having non-Newtonian rheology, in a porous microchannel was presented in this article. The governing mass transfer equation coupled with velocity field was solved along with associated boundary conditions using a similarity solution method. An analytical solution of mass transfer coefficient and hence, Sherwood number were derived from first principles. The corresponding effects of assisting and opposing pressure-driven flow and EOF were also analyzed. The influence of wall permeation, double-layer thickness, rheology, etc. on the mass transfer was also investigated. Permeation at the wall enhanced the mass transfer coefficient more than five times compared to impervious conduit in case of pressure-driven flow assisting the EOF at higher values of κh. Shear thinning fluid exhibited more enhancement of Sherwood number in presence of permeation compared to shear thickening one. The phenomenon of stagnation was observed at a particular κh (∼2.5) in case of EOF opposing the pressure-driven flow. This study provided a direct quantification of transport of a neutral solute in case of transdermal drug delivery, transport of drugs from blood to target region, etc.

Starch solutions, which are strongly non-Newtonian, show a surface instability, when subjected to a load. A droplet of the fluid is sandwiched between two glass plates and a weight varying from 1 to 5 kgs. is placed on the top plate. The area of contact between the fluid and plate increases in an oscillatory manner, unlike Newtonian fluids in a similar situation. The periphery moreover, develops a viscous fingering like instability, which is not expected under compression. We attempt to model...

Strongly non-Newtonianfluids namely, aqueous gels of starch, are shown to exhibit visco-elastic behavior, when subjected to a load. We study arrowroot and potato starch gels. When a droplet of the fluid is sandwiched between two glass plates and compressed, the area of contact between the fluid and plates increases in an oscillatory manner. This is unlike Newtonian fluids, where the area increases monotonically in a similar situation. The periphery moreover, develops an instability, which looks similar to Saffman Taylor fingers. This is not normally seen under compression. The loading history is also found to affect the manner of spreading. We attempt to describe the non-Newtonian nature of the fluid through a visco-elastic model incorporating generalized calculus. This is shown to reproduce qualitatively the oscillatory variation in the surface strain.

Strongly non-Newtonianfluids namely, aqueous gels of starch, are shown to exhibit visco-elastic behavior, when subjected to a load. We study arrowroot and potato starch gels. When a droplet of the fluid is sandwiched between two glass plates and compressed, the area of contact between the fluid and plates increases in an oscillatory manner. This is unlike Newtonian fluids, where the area increases monotonically in a similar situation. The periphery moreover, develops an instability, which looks similar to Saffman Taylor fingers. This is not normally seen under compression. The loading history is also found to affect the manner of spreading. We attempt to describe the non-Newtonian nature of the fluid through a visco-elastic model incorporating generalized calculus. This is shown to reproduce qualitatively the oscillatory variation in the surface strain.

Axial dispersion is an important parameter in the performance of packed bed reactors. A lot of fluids exhibit non-Newtonian behaviour but the effect of rheological parameters on axial dispersion is not available in literature. The effect of rheology on axial dispersion has been analysed for viscoinelastic and viscoelastic non-Newtonianfluids. Aqueous solutions of carboxymethyl cellulose and polyacrylamide have been chosen to represent viscoinelastic and viscoelastic liquid-phases. Axial dispersion has been measured in terms of BoL number. The single parameter axial dispersion model has been applied to analyse RTD response curve. The BoL numbers were observed to increase with increase in liquid flow rate and consistency index 'K' for viscoinelastic as well as viscoelastic fluids. Bodenstein correlation for Newtonian fluids proposed has been modified to account for the effect of fluid rheology. Further, Weissenberg number is introduced to quantify the effect of viscoelasticity.

In this paper, the unsteady pulsatile magneto-hydrodynamic blood flows through porous arteries concerning the influence of externally imposed periodic body acceleration and a periodic pressure gradient are numerically simulated. Blood is taken into account as the third-grade non-Newtonianfluid. Besides the numerical solution, for small Womersley parameter (such as blood flow through arterioles and capillaries), the analytical perturbation method is used to solve the nonlinear governing equations. Consequently, analytical expressions for the velocity profile, wall shear stress, and blood flow rate are obtained. Excellent agreement between the analytical and numerical predictions is evident. Also, the effects of body acceleration, magnetic field, third-grade non-Newtonian parameter, pressure gradient, and porosity on the flow behaviors are examined. Some important conclusions are that, when the Womersley parameter is low, viscous forces tend to dominate the flow, velocity profiles are parabolic in shape, and the center-line velocity oscillates in phase with the driving pressure gradient. In addition, by increasing the pressure gradient, the mean value of the velocity profile increases and the amplitude of the velocity remains constant. Also, when non-Newtonian effect increases, the amplitude of the velocity profile.

Gliding bacteria are an assorted group of rod-shaped prokaryotes that adhere to and glide on certain layers of ooze slime attached to a substratum. Due to the absence of organelles of motility, such as flagella, the gliding motion is caused by the waves moving down the outer surface of these rod-shaped cells. In the present study we employ an undulating surface model to investigate the motility of bacteria on a layer of non-Newtonian slime. The rheological behavior of the slime is characterized by an appropriate constitutive equation, namely the Carreau model. Employing the balances of mass and momentum conservation, the hydrodynamic undulating surface model is transformed into a fourth-order nonlinear differential equation in terms of a stream function under the long wavelength assumption. A perturbation approach is adopted to obtain closed form expressions for stream function, pressure rise per wavelength, forces generated by the organism and power required for propulsion. A numerical technique based on an implicit finite difference scheme is also employed to investigate various features of the model for large values of the rheological parameters of the slime. Verification of the numerical solutions is achieved with a variational finite element method (FEM). The computations demonstrate that the speed of the glider decreases as the rheology of the slime changes from shear-thinning (pseudo-plastic) to shear-thickening (dilatant). Moreover, the viscoelastic nature of the slime tends to increase the swimming speed for the shear-thinning case. The fluid flow in the pumping (generated where the organism is not free to move but instead generates a net fluid flow beneath it) is also investigated in detail. The study is relevant to marine anti-bacterial fouling and medical hygiene biophysics.

During the resent years several publications (for instance Hyzyak and Koelling, J. Non-Newt. Fluid Mech. 71,73-88 (1997) and Gauri and Koelling, Rheol. Acta, 38, 458-470 (1999)) have concerned gas assisted displacement of viscoelastic fluids (polymer melts and polymeric solutions) contained...... in a circular cylinder. This is a simple model system used to investigate the gas-fluid displacement, as the problem is reduced to an axis-symmetric flow problem. The understanding of this process is relevant for the geometrically much more complex polymer processing operation Gas-assisted injection moulding...

The rheology and molecular structure of a model bitumen (Cooee bitumen) under shear are investigated in the non-Newtonian regime using non-equilibrium molecular dynamics simulations. The shear viscosity, normal stress differences, and pressure of the bitumen mixture are computed at different shear rates and different temperatures. The model bitumen is shown to be a shear-thinning fluid at all temperatures. In addition, the Cooee model is able to reproduce experimental results showing the formation of nanoaggregates composed of stacks of flat aromatic molecules in bitumen. These nanoaggregates are immersed in a solvent of saturated hydrocarbon molecules. At a fixed temperature, the shear-shinning behavior is related not only to the inter- and intramolecular alignments of the solvent molecules but also to the decrease of the average size of the nanoaggregates at high shear rates. The variation of the viscosity with temperature at different shear rates is also related to the size and relative composition of the nanoaggregates. The slight anisotropy of the whole sample due to the nanoaggregates is considered and quantified. Finally, the position of bitumen mixtures in the broad literature of complex systems such as colloidal suspensions, polymer solutions, and associating polymer networks is discussed.

In recent years non-normality and transient growths have attracted much interest in fluid mechanics. Here, we investigate these topics with reference to the problem of interfacial instability in superposed Newtonian and non-Newtonianfluid layers. Under the hypothesis of the lubrication theory, we demonstrate the existence of significant transient growths in the parameter space region where the dynamical system is asymptotically stable, and show how they depend on the main physical parameters...

The nonsimilar boundary-layer analysis of steady laminar mixed-convection heat transfer between a vertical plate and non-Newtonianfluids is extended and unified. A mixed-convection parameter zeta is proposed to replace the conventional Richardson number, Gr/Re(exp 2/(2 - n)) and to serve as a controlling parameter that determines the relative importance of the forced and the free convection. The value of mixed-convection parameter lies between 0 and 1. In addition, the power-law model is used for non-Newtonianfluids with exponent n less than 1 for pseudoplastics; n = 1 for Newtonian fluids; and n greater than 1 for dilatant fluids. Furthermore, the coordinates and dependent variables are transformed to yield computationally efficient numerical solutions that are valid over the entire range of mixed convection, from the pure forced-convection limit to the pure free-convection limit, and the whole domain of non-Newtonianfluids, from pseudoplastics to dilatant fluids. The effects of the mixed-convection parameter, the power-law viscosity index, and the generalized Prandtl number on the velocity profiles, the temperature profiles, as well as on the wall skin friction and heat transfer rate are clearly illustrated for both cases of buoyancy assisting and opposing flow conditions.

Gravity driven instabilities in model porous packings of 1 mm diameter spheres are studied by comparing the broadening of the displacement front between fluids of slightly different densities in stable and unstable configurations. Water, water-glycerol and water-polymer solutions are used to vary independently viscosity and molecular diffusion and study the influence of shear-thinning properties. Both injected and displaced solutions are identical but for a different concentration of NaNO 3 salt used as an ionic tracer and to introduce the density contrast. Dispersivity in stable configuration increases with polymer concentration - as already reported for double porosity packings of porous grains. Gravity-induced instabilities are shown to develop below a same threshold Péclet number Pe for water and water-glycerol solutions of different viscosities and result in considerable increases of the dispersivity. Measured threshold Pe values decrease markedly on the contrary with polymer concentration. The quantitative analysis demonstrates that the development of the instabilities is controlled by viscosity through a characteristic gravity number G (ratio between hydrostatic and viscous pressure gradients). A single threshold value of G accounts for results obtained on Newtonian and non-Newtonian solutions.

The turbulence behavior of gas-liquid two-phase flow plays an important role in heat transfer and mass transfer in many chemical processes. In this work, a 2D particle image velocimetry (PIV) was used to investigate the turbulent characteristic of fluid induced by a chain of bubbles rising in Newtonian and non-Newtonianfluids. The instantaneous flow field, turbulent kinetic energy (TKE) and TKE dissipation rate were measured. The results demonstrated that the TKE profiles were almost symmetrical along the column center and showed higher values in the central region of the column. The TKE was enhanced with the increase of gas flow and decrease of liquid viscosity. The maximum TKE dissipation rate appeared on both sides of the bubble chain, and increased with the increase of gas flow rate or liquid viscosity. These results provide an understanding for gas-liquid mass transfer in non-Newtonianfluids.

A numerical study on incompressible laminar flow in symmetric channel with sudden expansion is conducted. In this work, Newtonian and non-Newtonianfluids are considered, where non-Newtonianfluids are described by the power-law model. Three different computational methods are employed, namely a semi-implicit Chorin projection method (SICPM), an explicit algorithm based on fourth-order Runge-Kutta method (ERKM) and a Lattice Boltzmann method (LBM). The aim of the work is to investigate on the capabilities of the LBM for the solution of complex flows through the comparison with traditional computational methods. In the range of Reynolds number investigated, excellent agreement with the literature results is found. In particular, the LBM is found to be accurate in the prediction of the fluid flow behavior for the problem under consideration.

(GAIM). This is a process, where a mould is filled partly with a polymer melt followed by the injection of inert gas into the core of the polymer melt. The numerical analysis of the fluid flow concerning the experimental observations data in these publications is all based on Newtonian or general......-B constitutive model will be used throughout this paper. A numerical method is needed in order to calculate the flow of the viscoelastic fluid during the displacement. To model the displacement numerically, the time-dependent finite element method from Rasmussen [1] is used. This method has second order...... convergence both in the time and the spatial discretization. The non-dimensional geometrical groups in this displacement are the Deborah and the surface elasticity number. The Deborah number is in a general definition (e.g. independent of constitutive equation) given as De=(2·U/R)·Ø1(2·U/R)/(2·çp(2·U...

This paper focuses on solution of numerical model for fluid film lubrication problem related to hydrodynamics with non-Newtonianfluid. A programming code is developed to investigate the effect of bearing design parameter such as pressure. A physical problem is modeled by a contact point of sphere on a disc with certain assumption. A finite difference method with staggered grid is used to improve the accuracy. The results show that the fluid characteristics as defined by power law fluid have led to a difference in the fluid pressure profile. Therefore a lubricant with special viscosity can reduced the pressure near the contact area of bearing.

Engineering inertial lift forces and elastic lift forces is explored to transfer microparticles across laminar streams from non-Newtonian to Newtonian fluid. A co-stream of non-Newtonian flow loaded with microparticles (9.9 and 2.0 μm in diameter) and a Newtonian carrier medium flow in a straight rectangular conduit is devised. The elastic lift forces present in the non-Newtonianfluid, undeterred by particle-particle interaction, successfully pass most of the larger (9.9 μm) particles over to the Newtonian fluid. The Newtonian fluid takes over the larger particles and focus them on the equilibrium position, separating the larger particles from the smaller particles. This mechanism enabled processing of densely suspended particle samples. The method offers dilution-free (for number densities up to 10,000 μL(-1)), high throughput (6700 beads/s), and highly efficient (>99% recovery rate, >97% purity) particle separation operated over a wide range of flow rate (2 orders of magnitude).

Data from FDA's nozzle challenge-a study to assess the suitability of simulating fluid flow in an idealized medical device-is used to validate the simulations obtained from a numerical, finite-differences code. Various physiological indicators are computed and compared with experimental data from three different laboratories, getting a very good agreement. Special care is taken with the derivation of blood damage (hemolysis). The paper is focused on the laminar regime, in order to investigate non-Newtonian effects (non-constant fluid viscosity). The code can deal with these effects with just a small extra computational cost, improving Newtonian estimations up to a ten percent. The relevance of non-Newtonian effects for hemolysis parameters is discussed.

Full Text Available The problem of steady, laminar, thermal Marangoni convection flow of non-Newtonian power law fluid along a horizontal surface with variable surface temperature is studied. The partial differential equations are transformed into ordinary differential equations by using a suitable similarity transformation and analytical approximate solutions are obtained by an efficient transformation, asymptotic expansion and Padé approximants technique. The effects of power law index and Marangoni number on velocity and temperature profiles are examined and discussed.

Heat transfer studies to Newtonian and non-Newtonianfluids are carried out in a stirred vessel fitted with anchor/turbine impeller and a coil for heating/cooling with an objective of determining experimentally the heat transfer coefficient of few industrially important systems namely castor oil and its methyl esters, soap solution, CMC and chalk slurries. The effect of impeller geometry, speed and aeration is investigated. Generalized Reynolds and Prandtl numbers are calculated using an apparent viscosity for non-Newtonianfluids. The data is correlated using a Sieder-Tate type equation. A trend of increase in heat transfer coefficient with RPM in presence and absence of solids has been observed. Relatively high values of Nusselt numbers are obtained for non-Newtonianfluids when aeration is coupled with agitation. The contribution of natural convection to heat transfer has been accounted for by incorporating the Grashof number. The correlations developed based on these studies are applied for design of commercial scale soponification reactor. Power per unit volume resulted in reliable design of a reactor.

A general mathematical model that predicts the flow fields in a mixed-flow anaerobic digester was developed. In this model, the liquid manure was assumed to be a non-Newtonianfluid, and the flow governed by the continuity, momentum, and k-epsilon standard turbulence equations, and non-Newtonian power law model. The commercial computational fluid dynamics (CFD) software, Fluent, was applied to simulate the flow fields of lab-scale, scale-up, and pilot-scale anaerobic digesters. The simulation results were validated against the experimental data from literature. The flow patterns were qualitatively compared for Newtonian and non-Newtonianfluids flow in a lab-scale digester. Numerical simulations were performed to predict the flow fields in scale-up and pilot-scale anaerobic digesters with different water pump power inputs and different total solid concentration (TS) in the liquid manure. The optimal power inputs were determined for the pilot-scale anaerobic digester. Some measures for reducing dead and low velocity zones were proposed based upon the CFD simulation results.

Conventional rheological characterisation using nuclear magnetic resonance (NMR) typically utilises spatially-resolved measurements of velocity. We propose a new approach to rheometry using pulsed field gradient (PFG) NMR which readily extends the application of MR rheometry to single-axis gradient hardware. The quantitative use of flow propagators in this application is challenging because of the introduction of artefacts during Fourier transform, which arise when realistic sampling strategies are limited by experimental and hardware constraints and when particular spatial and temporal resolution are required. The method outlined in this paper involves the cumulant analysis of the acquisition data directly, thereby preventing the introduction of artefacts and reducing data acquisition times. A model-dependent approach is developed to enable the pipe-flow characterisation of fluids demonstrating non-Newtonian power-law rheology, involving the use of an analytical expression describing the flow propagator in terms of the flow behaviour index. The sensitivity of this approach was investigated and found to be robust to the signal-to-noise ratio (SNR) and number of acquired data points, enabling an increase in temporal resolution defined by the SNR. Validation of the simulated results was provided by an experimental case study on shear-thinning aqueous xanthan gum solutions, whose rheology could be accurately characterised using a power-law model across the experimental shear rate range of 1-100 s(-1). The flow behaviour indices calculated using this approach were observed to be within 8% of those obtained using spatially-resolved velocity imaging and within 5% of conventional rheometry. Furthermore, it was shown that the number of points sampled could be reduced by a factor of 32, when compared to the acquisition of a volume-averaged flow propagator with 128 gradient increments, without negatively influencing the accuracy of the characterisation, reducing the

Full Text Available Introduction. The problems of simulating viscoplastic longitudinal and cross-sectional flow of non-Newtonianfluids are overviewed. Materials and methods. For the first time the superposition method by expressing the components of the stress tensor for building flow fields with higher dimension from flow fields with lower dimension with various boundary conditions when rheological parameters change depending on pressure was used. The flows in the channel are categorized by velocity and pressure values in each point of the section. Results.The theoretical methods for simulating flows of non-Newtonianfluids in channels of different geometry with moving bounds and pressure drop on channel edges with respect to functional connections between main process parameters are described using the superposition method. It is shown that longitudinal and cross-sectional are reduced to the collection of one-dimensional longitudinal flows of the same type which allow to describe three-dimensional isothermal in rectangular channel and two-dimensional flows in flat channels with different channel aspect ratio. The received theoretical two- and three-dimensional model of viscous flows in channels with basic geometry allow to research main regularities of the process and to establish optimal macro-kinetic and macro-dynamic flow characteristics of non-Newtonian materials which are aimed at reducing energy costs and material consumption of food processing equipment. Conclusion.The developed and theoretically reasonable three-dimensional models flows of non-Newtonianfluids in channels allow to perform qualitatively new design of food processing equipment which allows to reduce energy costs and material consumption.

Many industrial feeds behave as non-Newtonianfluids, and little understanding exists as to their influence on cross-flow microfiltration (CMF) performance. The viscosity effects of a model non-Newtonianshear-thickening fluid were investigated in CMF with and without suspended silica particles in t

Many industrial feeds behave as non-Newtonianfluids, and little understanding exists as to their influence on cross-flow microfiltration (CMF) performance. The viscosity effects of a model non-Newtonianshear-thickening fluid were investigated in CMF with and without suspended silica particles in

Dynamic wetting is an important interfacial phenomenon in many industrial applications. There have been many excellent reviews of dynamic wetting, especially on super-hydrophobic surfaces with physical or chemical coatings, porous layers, hybrid micro/nano structures and biomimetic structures. This review summarizes recent research on dynamic wetting from the viewpoint of the fluids rather than the solid surfaces. The reviewed fluids range from simple Newtonian fluids to non-Newtonianfluids and complex nanofluids. The fundamental physical concepts and principles involved in dynamic wetting phenomena are also reviewed. This review focus on recent investigations of dynamic wetting by non-Newtonianfluids, including the latest experimental studies with a thorough review of the best dynamic wetting models for non-Newtonianfluids, to illustrate their successes and limitations. This paper also reports on new results on the still fledgling field of nanofluid wetting kinetics. The challenges of research on nanofluid dynamic wetting is not only due to the lack of nanoscale experimental techniques to probe the complex nanoparticle random motion, but also the lack of multiscale experimental techniques or theories to describe the effects of nanoparticle motion at the nanometer scale (10(-9) m) on the dynamic wetting taking place at the macroscopic scale (10(-3) m). This paper describes the various types of nanofluid dynamic wetting behaviors. Two nanoparticle dissipation modes, the bulk dissipation mode and the local dissipation mode, are proposed to resolve the uncertainties related to the various types of dynamic wetting mechanisms reported in the literature.

Full Text Available A study is made of non-Newtonian HHD aligned steady plane fluid flows to find exact solutions for various flow configurations. The equations of motion have been transformed to the hodograph plane. A Legendre-transform function is used to recast the equations in the hodograph plane in terms of this transform function. Solutions for various flow configurations are obtained. Applications are investigated for the fluids of finite and infinite electrical conductivity bringing out the similarities and contrasts in the solutions of these types of fluids.

It is well known that when a flexible or flexibly-mounted structure is placed perpendicular to the flow of a Newtonian fluid, it can oscillate due to the shedding of separated vortices at high Reynolds numbers. If the same flexible object is placed in non-Newtonian flows, however, the structure's response is still unknown. Unlike Newtonian fluids, the flow of viscoelastic fluids can become unstable at infinitesimal Reynolds numbers due to a purely elastic flow instability. In this talk, we will present a series of experiments investigating the response of a flexible cylinder placed in the cross flow of a viscoelastic fluid. The elastic flow instabilities occurring at high Weissenberg numbers can exert fluctuating forces on the flexible cylinder thus leading to nonlinear periodic oscillations of the flexible structure. These oscillations are found to be coupled to the time-dependent state of viscoelastic stresses in the wake of the flexible cylinder. The static and dynamic responses of the flexible cylinder will be presented over a range of flow velocities, along with measurements of velocity profiles and flow-induced birefringence, in order to quantify the time variation of the flow field and the state of stress in the fluid.

In this paper, we computed fluid pressure and force on fascia sheets during manual therapy treatments using Squeeze Film Lubrication theory for non-Newtonianfluids. For this purpose, we developed a model valid for three dimensional fluid flow of a non-Newtonian liquid. Previous models considered only one-dimensional flows in two dimensions. We applied this model to compare the one-dimensional flow of HA, considered as a lubricating fluid, around or within the fascia during sliding, vibration, and back-and-forth sliding manipulation treatment techniques. The fluid pressure of HA increases dramatically as fascia is deformed during manual therapies. The fluid force increases more during vertical vibratory manipulation treatment than in constant sliding, and back and forth motion. The variation of fluid pressure/force causes HA to flow near the edges of the fascial area under manipulation in sliding and back and forth motion which may result in greater lubrication. The fluid pressure generated in manual therapy techniques may improve sliding and permit muscles to work more efficiently.

Full Text Available The purpose of this paper is to study the performance of a finite length journal bearing, taking into account effects of non-Newtonian Rabinowitsch flow rheology and elastic deformations of the bearing liner. According to the Rabinowitsch fluid model, the cubic-stress constitutive equation is used to account for the non-Newtonian effects of pseudoplastic and dilatant lubricants. Integrating the continuity equation across the film, the nonlinear non-Newtonian Reynolds-type equation is derived. The elasticity part of the problem is solved on the base of Vlassov model of an elastic foundation. The numerical solution of the modified Reynolds equation is carried out by using FDM with over-relaxation technique. The results for steady state bearing performance characteristics have been calculated for various values of nonlinear factor and elasticity parameters. It was concluded that in comparison with the Newtonian lubricants, higher values of film pressure and load carrying capacity have been obtained for dilatant lubricants, while the case was reversed for pseudoplastic lubricants.

On the basis of Navier-Stockes equation and convection-diffusion equation, combined with surface tension and penetration models, the equations of moment and mass transfer between bubble and the ambient non-Newtonian liquid were established. The formation of a single bubble from a submersed nozzle of 1.0 mm diameter and the mass transfer from an artificially fixed bubble into the ambient liquid were simulated by the volume-of-fluid （VOF） method. Good agreement between simulation results and experimental data confirmed the validity of the numerical method. Furthermore, the concentration distribution around rising bubbles in shear thinning non-Newtonianfluid was simulated. When the process of a single ellipsoidal bubble with the bubble deformation rate below 2.0 rises, the concentration distribution is a single-tail in the bubble＇s wake, but it is fractal when thebubble deformation rate is greater than 2.0. For the overtaking of two in-line rising bubbles, the concentration distribution area between two bubbles broadens gradually and then coalescence occurs. The bifurcation of concentration distribution appears in the rear of the resultant bubble.

Steady and pulsatile flows of Newtonian and non-Newtonianfluids through a 180°-curved pipe were investigated using particle image velocimetry (PIV). The experiment was inspired by physiological pulsatile flow through large curved arteries, with a carotid artery flow rate imposed. Sodium iodide (NaI) and sodium thiocyanate (NaSCN) were added to the working fluids to match the refractive index (RI) of the test section to eliminate optical distortion. Rheological measurements revealed that adding NaI or NaSCN changes the viscoelastic properties of non-Newtonian solutions and reduces their shear-thinning property. Measured centerline velocity profiles in the upstream straight pipe agreed well with an analytical solution. In the pulsatile case, secondary flow structures, i.e. deformed-Dean, Dean, Wall and Lyne vortices, were observed in various cross sections along the curved pipe. Vortical structures at each cross section were detected using the d2 vortex identification method. Circulation analysis was performed on each vortex separately during the systolic deceleration phase, and showed that vortices split and rejoin. Secondary flow structures in steady flows were found to be morphologically similar to those in pulsatile flows for sufficiently high Dean number. supported by the George Washington University Center for Biomimetics and Bioinspired Engineering.

In recent years non-normality and transient growths have attracted much interest in fluid mechanics. Here, we investigate these topics with reference to the problem of interfacial instability in superposed Newtonian and non-Newtonianfluid layers. Under the hypothesis of the lubrication theory, we demonstrate the existence of significant transient growths in the parameter space region where the dynamical system is asymptotically stable, and show how they depend on the main physical parameters. In particular, the key role of the density ratio is highlighted.

This paper focuses on the flow characteristic and local resistance of non-Newtonian power law fluid in a curved 90° bend pipe with circular cross-sections, which are widely used in industrial applications. By employing numerical simulation and theoretical analysis the properties of the flow and local resistance of power law fluid under different working conditions are obtained. To explore the change rule the experiment is carried out by changing the Reynolds number, the wall roughness and different diameter ratio of elbow pipe. The variation of the local resistance coefficient with the Reynolds number, the diameter ratio and the wall roughness is presented comprehensively in the paper. The results show that the local resistance force coefficient hardly changes with Reynolds number of the power law fluid; the wall roughness has a significant impact on the local resistance coefficient. As the pipe wall roughness increasing, the coefficient of local resistance force will increase. The main reason of the influence of the roughness on the local resistance coefficient is the increase of the eddy current region in the power law fluid flow, which increases the kinetic energy dissipation of the main flow. This paper provides theoretical and numerical methods to understand the local resistance property of non-Newtonian power law fluid in elbow pipes.

Numerical analyses of transient electro-osmosis of a typical non-Newtonian liquid induced by DC and AC electric fields in a rectangular microchannel are conducted in the framework of continuum fluid mechanics. The famous power-law constitutive model is used to express the fluid dynamic viscosity in terms of the velocity gradient. Transient start-up characteristics of electro-osmotic power-law liquid flow in rectangular microchannels are simulated by using finite element method. Under a DC electric field, it is found out and the fluid is more inert to the external electric field and the steady-state velocity profile becomes more plug-like with decrease of the flow behavior index of the power-law liquids. The numerical calculations also confirm the validity of the generalized Smoluchowski slip velocity which can serve as the counterpart for the classic Smoluchowski slip velocity when dealing with electrokinetic flow of non-Newtonian power-law fluids. Under AC electric fields, the fluid is more obviously acceler...

In this paper, 12 turbulence models for single-phase non-newtonianfluid flow in a pipe are evaluated by comparing the frictional pressure drops obtained from computational fluid dynamics (CFD) with those from three friction factor correlations. The turbulence models studied are (1) three high-Reynolds-number k-ε models, (2) six low-Reynolds-number k-ε models, (3) two k-ω models, and (4) the Reynolds stress model. The simulation results indicate that the Chang-Hsieh-Chen version of the low-Reynolds-number k-ε model performs better than the other models in predicting the frictional pressure drops while the standard k-ω model has an acceptable accuracy and a low computing cost. In the model applications, CFD simulation of mixing in a full-scale anaerobic digester with pumped circulation is performed to propose an improvement in the effective mixing standards recommended by the U.S. EPA based on the effect of rheology on the flow fields. Characterization of the velocity gradient is conducted to quantify the growth or breakage of an assumed floc size. Placement of two discharge nozzles in the digester is analyzed to show that spacing two nozzles 180° apart with each one discharging at an angle of 45° off the wall is the most efficient. Moreover, the similarity rules of geometry and mixing energy are checked for scaling up the digester.

This paper studies the pullback asymptotic behavior of solutions for the non-autonomous incompressible non-Newtonianfluid in 2D bounded domains. Firstly, with a little high regularity of the force, the semigroup method and ɛ -regularity method are used to establish the existence of compact pullback absorbing sets. Then, with a minimal regularity of the force, by verifying the flattening property also known as the "Condition (C)", the author proves the existence of pullback attractors for the universe of fixed bounded sets and for the another universe given by a tempered condition. Furthermore, the regularity of pullback attractors is given.

We study experimentally the acoustic signal associated with a continuous bubble bursting at the free surface of a non-Newtonianfluid. Due to the fluid rheological properties, the bubble shape is elongated, and, when bursting at the free surface, acts as a resonator. For a given fluid concentration, at constant flow rate, repetitive bubble bursting occurs at the surface. We report a modulation pattern of the acoustic waveform through time. Moreover, we point out the existence of a precursor acoustic signal, recorded on the microphone array, previous to each bursting. The time delay between this precursor and the bursting signal is well correlated with the bursting signal frequency content. Their joint modulation through time is driven by the fluid rheology, which strongly depends on the presence of small satellite bubbles trapped in the fluid due to the yield stress.

This article presents the evaluation of force effects on rotor of squeeze film damper. Rotor is eccentric placed and its motion is translate-circular. The amplitude of rotor motion is smaller than its initial eccentricity. The force effects are calculated from pressure and viscous forces which were gained by using computational modeling. Two types of fluid were considered as filling of damper. First type of fluid is Newtonian (has constant viscosity) and second type is magnetorheological fluid (does not have constant viscosity). Viscosity of non-Newtonianfluid is given using Bingham rheology model. Yield stress is a function of magnetic induction which is described by many variables. The most important variables of magnetic induction are electric current and gap width which is between rotor and stator. Comparison of application two given types of fluids is shown in results.

The study of flow of non-Newtonianfluids in porous media is very important and serves a wide variety of practical applications in processes such as enhanced oil recovery from underground reservoirs, filtration of polymer solutions and soil remediation through the removal of liquid pollutants. These fluids occur in diverse natural and synthetic forms and can be regarded as the rule rather than the exception. They show very complex strain and time dependent behavior and may have initial yield-stress. Their common feature is that they do not obey the simple Newtonian relation of proportionality between stress and rate of deformation. Non-Newtonianfluids are generally classified into three main categories: time-independent whose strain rate solely depends on the instantaneous stress, time-dependent whose strain rate is a function of both magnitude and duration of the applied stress and viscoelastic which shows partial elastic recovery on removal of the deforming stress and usually demonstrates both time and str...

This paper presents an Eulerian multiphase flow model that characterizes gas mixing in anaerobic digesters. In the model development, liquid manure is assumed to be water or a non-Newtonianfluid that is dependent on total solids (TS) concentration. To establish the appropriate models for different TS levels, twelve turbulence models are evaluated by comparing the frictional pressure drops of gas and non-Newtonianfluid two-phase flow in a horizontal pipe obtained from computational fluid dynamics (CFD) with those from a correlation analysis. The commercial CFD software, Fluent12.0, is employed to simulate the multiphase flow in the digesters. The simulation results in a small-sized digester are validated against the experimental data from literature. Comparison of two gas mixing designs in a medium-sized digester demonstrates that mixing intensity is insensitive to the TS in confined gas mixing, whereas there are significant decreases with increases of TS in unconfined gas mixing. Moreover, comparison of three mixing methods indicates that gas mixing is more efficient than mixing by pumped circulation while it is less efficient than mechanical mixing.

This paper examines pressure falloff behavior in fractured wells following the injection of a non-Newtonian power-law fluid. Results are presented in a form suitable for field application. Responses at wells intercepting infinite-conductivity and uniformflux fractures are considered. Procedures to identify flow regimes are discussed. The solutions presented here are new and to our knowledge not available in the literature. The consequences of neglecting the non-Newtonian characteristics of the injected fluid are examined. The results of this work were obtained by a finite difference model. Procedures to compute the apparent viscosity of power-law fluids for twodimensional flow through porous media are discussed. The formulation given here avoids numerical problems (multiple solutions, cross over, etc.) reported in other studies. Although, the main objective of the work is to examine pressure falloff behavior at fractured wells, the authors also examine responses at unfractured wells. The main objective of this part of a study is to examine the validity of using the superposition principle to analyze pressure falloff data. (The pressure distribution for this problem is governed by a nonlinear partial differential equation.) If the solutions given in the literature are used, then correction factors are needed to analyze pressure falloff data. The results of this phase of the work can also be used to analyze data in fractured wells provided that pseudoradial flow conditions exist.

Theoretical study of non-Newtonian effects of second-order fluids on the performance characteristics of inclined slider bearings is presented. An approximate method is used for the solution of the highly nonlinear momentum equations for the second-order fluids. The closed form expressions for the fluid film pressure, load carrying capacity, frictional force, coefficient of friction, and centre of pressure are obtained. The non-Newtonian second order fluid model increases the film pressure, load carrying capacity, and frictional force whereas the center of pressure slightly shifts towards exit region. Further, the frictional coefficient decreases with an increase in the bearing velocity as expected for an ideal fluid.

We investigate the flow of various non-newtonianfluids through three-dimensional disordered porous media by direct numerical simulation of momentum transport and continuity equations. Remarkably, our results for power-law (PL) fluids indicate that the flow, when quantified in terms of a properly modified permeability-like index and Reynolds number, can be successfully described by a single (universal) curve over a broad range of Reynolds conditions and power-law exponents. We also study the flow behavior of Bingham fluids described in terms of the Herschel-Bulkley model. In this case, our simulations reveal that the interplay of (i) the disordered geometry of the pore space, (ii) the fluid rheological properties, and (iii) the inertial effects on the flow is responsible for a substantial enhancement of the macroscopic hydraulic conductance of the system at intermediate Reynolds conditions.

A multiple parameter model to describe the Non-Newtonianproperties of fluid filtration in porous media is presented with regard to the pressure gradient expression in terms of the velocity of filtration, where the multiple parameters should be determined by measurements. Based on such a model, an analysis was furnished to deduce the formula for the rate of production of a oil well, and the governing equations for single phase Non-Newtonianfluid fritration. In order to examine the effects of model parameters, the governing equations were numerically solved with the method of cross-diagonal decomposition ZG method. It is found that, for constant rate of production, the power index n of the model influences the pressure distribution considerably, particularly in the vicinity of a single well. The well-bore pressure of Leibenzonian fluid is lower than that of the power-law fluid in the case of the same parameter B and the power index n = 0.5.

Non-equilibrium molecular dynamics simulations of an atomic fluid under shear flow, planar elongational flow, and a combination of shear and elongational flow are unified consistently with a tensorial model over a wide range of strain rates. A model is presented that predicts the pressure tensor for a non-Newtonian bulk fluid under a homogeneous planar flow field. The model provides a quantitative description of the strain-thinning viscosity, pressure dilatancy, deviatoric viscoelastic lagging, and out-of-flow-plane pressure anisotropy. The non-equilibrium pressure tensor is completely described through these four quantities and can be calculated as a function of the equilibrium material constants and the velocity gradient. This constitutive framework in terms of invariants of the pressure tensor departs from the conventional description that deals with an orientation-dependent description of shear stresses and normal stresses. The present model makes it possible to predict the full pressure tensor for a simple fluid under various types of flows without having to produce these flow types explicitly in a simulation or experiment.

A theoretical analysis for the laminar boundary layer flow of a non-Newtonianfluid on a continuous moving flat plate with surface strong suction/blowing is made. The types of potential flows necessary for similar solutions to the boundary layer are determined and both analytical and numerical solutions are presented. It is shown that the solution of the boundary layer problem depends not only on the ratio of the velocity of the plate to the velocity of the free stream, but also on the suction/blowing parameter. The skin friction decreases with increasing the parameters of power law and blowing. In the case of existing suction, the shear force decreases with the increases of tangential velocity, the largest shear force occurs at wall and the smallest shear force occurs at the edge of the boundary layer. However, in the case of existing surface blowing, the shear force initially increases with tangentialvelocity and the biggest shear force occurs at the interior of the boundary layer, the skin friction approaches to zero as the blowing rate approaches the critical value.

We conducted an experimental study of the interaction and coalescence of two drops (of the same fluid) or bubbles translating under the action of buoyancy in a cylindrical tube. The close approach of two Newtonian fluid particles of different size in a non-Newtonian continuous phase was examined using image analysis, and measurements of the coalescence time are reported for various particle size ratios, Bond numbers, and particle-to-suspending-fluid viscosity ratios. The flow disturbance behind the leading bubble and the viscoelastic nature of the continuous phase seemed to retard bubble coalescence. The time scale for coalescence of liquid drops in highly elastic continuous phase was influenced by the relative motion of the drops and their coalescence behavior.

The nucleation and propagation of hydrofractures by injection of over pressured fluids in an elastic and isotropic medium are studied experimentally. Non-Newtonianfluids are injected inside a gelatine whose mechanical properties are assumed isotropic at the experimental strain rates. Linear elastic theory predicts that plastic deformation associated to breakage of gelatin bonds is limited to a small zone ahead of the tip of the propagating fracture and that propagation will be maintained while the fluid pressure exceeds the normal stress to the fracture walls (Ch\\'avez-\\'Alvarez,2008) (i.e., the minimum compressive stress), resulting in a single mode I fracture geometry. However, we observed the propagation of fractures type II and III as well as nucleation of secondary fractures, with oblique to perpendicular trajectories with respect to the initial fracture. In the Video (http://hdl.handle.net/1813/14122) experimental evidence shows that the fracture shape depends on the viscoelastic properties of gelatine...

efficient, allowing simulations of tens of thousands of rigid particles within a reasonable computational time. Furthermore, the framework does not require any fitting constants or parameters devoid of a clear physical meaning and it is stable, robust and can be easily generalized to a variety of problems......A numerical framework capable of predicting the free surface flow of a suspension of rigid particles in a non-Newtonianfluid is described. The framework is a combination of the lattice Boltzmann method for fluid flow, the mass tracking algorithm for free surface representation, the immersed...... boundary method for two-way coupled interactions between fluid and rigid particles and an algorithm for the dynamics and mutual interactions of rigid particles. The framework is able to simulate the flow of suspensions at the level of the largest suspended particles and, at the same time, the model is very...

In this paper, a finite difference scheme is developed to solve the unsteady problem of combined heat and mass transfer from an isothermal curved surface to a porous medium saturated by a non-Newtonianfluid. The curved surface is kept at constant temperature and the power-law model is used to model the non-Newtonianfluid. The explicit finite difference method is used to solve simultaneously the equations of momentum, energy and concentration. The consistency of the explicit scheme is examined and the stability conditions are determined for each equation. Boundary layer and Boussinesq approximations have been incorporated. Numerical calculations are carried out for the various parameters entering into the problem. Velocity, temperature and concentration profiles are shown graphically. It is found that as time approaches infinity, the values of wall shear, heat transfer coefficient and concentration gradient at the wall, which are entered in tables, approach the steady state values.

In this work, we consider a non-Newtonianfluid flow in perforated domains. Fluid flow in perforated domains have a multiscale nature and solution techniques for such problems require high resolution. In particular, the discretization needs to honor the irregular boundaries of perforations. This gives rise to a fine-scale problems with many degrees of freedom which can be very expensive to solve. In this work, we develop a multiscale approach that attempt to solve such problems on a coarse grid by constructing multiscale basis functions. We follow Generalized Multiscale Finite Element Method (GMsFEM) [1, 2] and develop a multiscale procedure where we identify multiscale basis functions in each coarse block using snapshot space and local spectral problems [3, 4]. We show that with a few basis functions in each coarse block, one can accurately approximate the solution, where each coarse block can contain many small inclusions.

In this paper, the fountain flow of a non-Newtonianfluid during the filling of a plane vertical channel with due account of dissipative heating is investigated. The rheological features of the medium are defined by Ostwald de Waele power-law with exponential temperature dependence of viscosity. The numerical solution of the problem is obtained using a finite-difference method, based on the SIMPLE algorithm, and the method of invariants for compliance with the natural boundary conditions on free surface. It was shown that the flow separates into a two-dimensional flow zone in the vicinity of the free surface and a onedimensional flow zone away from it. The parametrical investigations of kinematic and thermophysical properties of the flow and the dependence of the free surface behavior on the basic criteria and rheological parameters are implemented.

We deal with a variational inequality describing the motion of incompressible fluids, whose viscous stress tensors belong to the subdifferential of a functional at the point given by the symmetric part of the velocity gradient, with a nonlocal friction condition on a part of the boundary obtained by a generalized mollification of the stresses. We establish an existence result of a solution to the nonlocal friction problem for this class of non-Newtonian flows. The result is based on the Faedo-Galerkin and Moreau-Yosida methods, the duality theory of convex analysis and the Tychonov-Kakutani-Glicksberg fixed point theorem for multi-valued mappings in an appropriate functional space framework.

The problem of the boundary layer flow of power law non-Newtonianfluids with a novel boundary condition is studied. The existence and uniqueness of the solutions are examined, which are found to depend on the curvature of the solutions for different values of the power law index n. It is established with the aid of the Picard-Lindel¨of theorem that the nonlinear boundary value problem has a unique solution in the global domain for all values of the power law index n but with certain conditions on the curva-ture of the solutions. This is done after a suitable transformation of the dependent and independent variables. For 0 1, the solution has a negative or zero curvature on some part of the global domain. Some solutions are presented graphically to illustrate the results and the behaviors of the solutions.

Full Text Available In the present study, the first and second law analyses of power-law non-Newtonian flow over embedded open parallel microchannels within micropatterned permeable continuous moving surface are examined at prescribed surface temperature. A similarity transformation is used to reduce the governing equations to a set of nonlinear ordinary differential equations. The dimensionless entropy generation number is formulated by an integral of the local rate of entropy generation along the width of the surface based on an equal number of microchannels and no-slip gaps interspersed between those microchannels. The velocity, the temperature, the velocity gradient, and the temperature gradient adjacent to the wall are substituted into this equation resulting from the momentum and energy equations obtained numerically by Dormand-Prince pair and shooting method. Finally, the entropy generation numbers, as well as the Bejan number, are evaluated. It is noted that the presence of the shear thinning (pseudoplastic fluids creates entropy along the surface, with an opposite effect resulting from shear thickening (dilatant fluids.

Full Text Available An analytical investigation is applied for unsteady motion of a rigid spherical particle in a quiescent shear-thinning power-law fluid. The results were compared with those obtained from Collocation Method (CM and the established Numerical Method (Fourth order Runge–Kutta scheme. It was shown that CM gave accurate results. Collocation Method (CM and Numerical Method are used to solve the present problem. We obtained that the CM which was used to solve such nonlinear differential equation with fractional power is simpler and more accurate than series method such as HPM which was used in some previous works by others but the new method named Akbari-Ganji’s Method (AGM is an accurate and simple method which is slower than CM for solving such problems. The terminal settling velocity—that is the velocity at which the net forces on a falling particle eliminate—for three different spherical particles (made of plastic, glass and steel and three flow behavior index n, in three sets of power-law non-Newtonianfluids was investigated, based on polynomial solution (CM. Analytical results obtained indicated that the time of reaching the terminal velocity in a falling procedure is significantly increased with growing of the particle size that validated with Numerical Method. Further, with approaching flow behavior to Newtonian behavior from shear-thinning properties of flow (n → 1, the transient time to achieving the terminal settling velocity is decreased.

Initially 3D FEM simulation of a simplified mixer was used to examine the effect of mixer configuration and operating conditions on dispersive mixing of a non-Newtonianfluid. Horizontal and vertical velocity magnitudes increased with increasing mixer speed, while maximum axial velocity and shear rate were greater with staggered paddles. In contrast, parallel paddles produced an area of efficient dispersive mixing between the center of the paddle and the barrel wall. This study was expanded to encompass the complete nine-paddle mixing section using power-law and Bird-Carreau fluid models. In the center of the mixer, simple shear flow was seen, corresponding with high [special character omitted]. Efficient dispersive mixing appeared near the barrel wall at all flow rates and near the barrel center with parallel paddles. Areas of backflow, improving fluid retention time, occurred with staggered paddles. The Bird-Carreau fluid showed greater influence of paddle motion under the same operating conditions due to the inelastic nature of the fluid. Shear-thinning behavior also resulted in greater maximum shear rate as shearing became easier with decreasing fluid viscosity. Shear rate distributions are frequently calculated, but extension rate calculations have not been made in a complex geometry since Debbaut and Crochet (1988) defined extension rate as the ratio of the third to the second invariant of the strain rate tensor. Extension rate was assumed to be negligible in most studies, but here extension rate is shown to be significant. It is possible to calculate maximum stable bubble diameter from capillary number if shear and extension rates in a flow field are known. Extension rate distributions were calculated for Newtonian and non-Newtonianfluids. High extension and shear rates were found in the intermeshing region. Extension is the major influence on critical capillary number and maximum stable bubble diameter, but when extension rate values are low shear rate has

A theoretical analysis for the boundary layer flow over a continuous moving surface in an otherwise quiescent pseudo-plastic non-Newtonianfluid medium was presented. The types of potential flows necessary for similar solutions to the boundary layer equations were determined and the solutions were numerically presented for different values of power law exponent.

ESDU 91025 discusses models used to describe the rheology of time independent pseudohomogeneous non-Newtonianfluids (power-law, Bingham, Herschel-Bulkley and a generalized model due to Metzner and Reed); they are used to calculate the laminar flow pressure drop (which is independent of pipe roughness in this regime). Values of a generalized Reynolds number are suggested to define transitional and turbulent flow. For turbulent flow in smooth pipes, pressure loss is estimated on the basis of an experimentally determined rheogram using either the Dodge-Metzner or Bowen approach depending on the available measurements. Bowen requires results for at least two pipe diameters. The choice of Dodge-Metzner when data are limited is discussed; seven possible methods are assessed against five sets of experimental results drawn from the literature. No method is given for transitional flow, which it is suggested should be avoided, but the turbulent correlation is recommended because it will yield an overestimate. Suggestions are made for the treatment of roughness effects. Several worked examples illustrate the use of the methods and a flowchart guides the user through the process from experimentally characterizing the behavior of the fluid to determining the pressure drop. A computer program, ESDUpac A9125, is also provided.

It has been recognized that fluid-structure interactions (FSI) play an important role in cardiovascular disease initiation and development. However, in vivo MRI multi-component FSI models for human carotid atherosclerotic plaques with bifurcation and quantitative comparisons of FSI models with fluid-only or structure-only models are currently lacking in the literature. A 3D non-Newtonian multi-component FSI model based on in vivo/ex vivo MRI images for human atherosclerotic plaques was introduced to investigate flow and plaque stress/strain behaviors which may be related to plaque progression and rupture. Both artery wall and plaque components were assumed to be hyperelastic, isotropic, incompressible and homogeneous. Blood flow was assumed to be laminar, non-Newtonian, viscous and incompressible. In vivo/ex vivo MRI images were acquired using histologically-validated multi-spectral MRI protocols. The 3D FSI models were solved and results were compared with those from a Newtonian FSI model and wall-only/fluid-only models. A 145% difference in maximum principal stresses (Stress-P(1)) between the FSI and wall-only models and 40% difference in flow maximum shear stress (MSS) between the FSI and fluid-only models were found at the throat of the plaque using a severe plaque sample (70% severity by diameter). Flow maximum shear stress (MSS) from the rigid wall model is much higher (20-40% in maximum MSS values, 100-150% in stagnation region) than those from FSI models.

The problem of the morphological stability of an interface in the case of the displacement of one non-Newtonianfluid by another non-Newtonianfluid in a radial Hele-Shaw cell has been considered. Both fluids have been described by the two-parameter Ostwald-de Waele power-law model. The nonzero viscosity of the displacing fluid has been taken into account. A generalized Darcy's law for the system under consideration, as well as an equation for the determination of the critical size of morphological stability with respect to harmonic perturbations (linear analysis), has been derived. Morphological phase diagrams have been constructed, and the region of the parameters in which nonequilibrium reentrant morphological transitions are possible has been revealed.

Full Text Available The construction process of a viscometer, developed in collaboration with a final project student, is here presented. It is intended to be used by first year's students to know the viscosity as a fluid property, for both Newtonian and non-Newtonian flows. Viscosity determination is crucial for the fluids behaviour knowledge related to their reologic and physical properties. These have great implications in engineering aspects such as friction or lubrication. With the present experimental model device three different fluids are analyzed (water, kétchup and a mixture with cornstarch and water. Tangential stress is measured versus velocity in order to characterize all the fluids in different thermal conditions. A mathematical fit process is proposed to be done in order to adjust the results to expected analytical expressions, obtaining good results for these fittings, with R2 greater than 0.88 in any case.

The article contains results of the experimental studies on atomization process of inhaled drugs and aqueous solutions of glycerol with aqueous solutions of glycerol polyacrylamide (Rokrysol WF1) in pneumatic nebulizers. In experiments, the different concentration of aqueous solutions of glycerol polyacrylamide have been tested. In addition, the effect of nebulizer design on atomization process has been determined. The one of the main elements of medical pneumatic nebulizer is nebulizer cup. The experiment with this scope is new and is very important from the point of view of aerosol therapy. The results have been obtained by the use of the digital microphotography technique. In order to determine a physicochemical properties of tested liquids, a rheological measurements and measurements of the surface tension were carried out. The differences between characteristics of aerosol for the liquids have been observed. The analysis of the droplets size distributions shows that the different diameters of droplets for Newtonian and non-Newtonianfluids have been formed during atomization in pneumatic nebulizers equipped with different nebulizer cups. The effect of the mouthpiece location on the droplets diameters has been shown. Precise design of nebulizer and nebulizer cups, and also physicochemical properties of atomized liquids are of high importance in order to the effectiveness of drug delivery to patient's respiratory tracts.

Full Text Available This study studied the flow characteristic of non-newtonian in eccentric annulus of highly-deviated well. On the basis of dimensionless analysis of motion equations and continuity equation, Hele-Shaw model suitable for fluid flow in the annulus was derived. Combined with H-B rheological model, velocity and stream distribution model were founded and calculated by numerical method. Furthermore, two-dimensional flow characteristic in eccentric annulus was got and the influence of different factors (such as yield stress, pressure gradient or eccentricity on velocity distribution in condition of laminar flow was analyzed. Width of flow core in the annular is proportional to yield stress and inversely proportional to pressure gradient. In eccentric annulus, eccentricity influences the stream distribution remarkably: with the increment of eccentricity, the contour lines of stream function gradually centralize in the widest annular gap, however distribute the most loosely in the narrowest annular gap. Axial velocity is the largest in the widest gap. The larger eccentricity is, the larger contrast of axial velocity between in the widest gap and in the narrowest gap is. There is the largest azimuthal velocity in an annular gap of a certain azimuthal angle, however which equals to zero in the widest and narrowest annular gap separately. The larger eccentricity is, the more homogeneous azimuthal velocity is. The velocity contrast in the entire annulus can be smoothed by increasing pressure gradient, power law index or decreasing yield stress.

In this paper, fractional order derivative, fractal dimension and spectral dimension are introduced into the seepage flow mechanics to establish the relaxation models of non-Newtonian viscoelastic fluids with the fractional derivative in fractal reservoirs. A new type integral transform is introduced, and the flow characteristics of non-Newtonian viscoelastic fluids with the fractional order derivative through a fractal reservoir are studied by using the integral transform, the discrete Laplace transform of sequential fractional derivatives and the generalized Mittag-Leffler function. Exact solutions are obtained for arbitrary fractional order derivative. The long-time and short-time asymptotic solutions for an infinite formation are also obtained. The pressure transient behavior of non-Newtonian viscoelastic fluids flow through an infinite fractal reservoir is studied by using the Stehfest's inversion method of the numerical Laplace transform. It is shown that the clearer the viscoelastic characteristics of the fluid, the more the fluid is sensitive to the order of the fractional derivative. The new type integral transform provides a new analytical tool for studying the seepage mechanics of fluid in fractal porous media.

In this paper we consider the Stochastic isothermal, nonlinear, incompressible bipolar viscous fluids driven by a genuine cylindrical fractional Bronwnian motion with Hurst parameter $H \\in (1/4,1/2)$ under Dirichlet boundary condition on 2D square domain. First we prove the existence and regularity of the stochastic convolution corresponding to the stochastic non-Newtonianfluids. Then we obtain the existence and uniqueness results for the stochastic non-Newtonianfluids. Under certain condition, the random dynamical system generated by non-Newtonianfluids has a random attractor.

The spreading dynamics of power-law fluids, both shear-thinning and shear-thickening fluids, that completely or partially wet solid substrate was investigated theoretically and experimentally. An evolution equation for liquid-film thickness was derived using a lubrication approximation, from which the dynamic contact angle versus the contact line moving velocity relationship was evaluated. In the capillary spreading regime, film thickness h is proportional to xi3/(n+2) (xi is the distance from the contact line), whereas in the gravitational regime, h is proportional to xi1/(n+2), relating to the rheological power exponent n. The derived model fit the experimental data well for a shear-thinning fluid (0.2% w/w xanthan solution) or a shear-thickening fluid (7.5% w/w 10 nm silica in polypropylene glycol) on a completely wetted substrate. The derived model was extended using Hoffmann's proposal for partially wetting fluids. Good agreement was also attained between model predictions and the shear-thinning fluid (1% w/w cmc solution) and shear-thickening fluid (10% w/w 15 nm silica) on partially wetted surfaces.

This paper describes a mathematical model of the main fracture isolation in porous media by water-based mature gels. While modeling injection, water infiltration from the gel pack through fracture walls is taking into account, due to which the polymer concentration changes and the residual water resistance factor changes as a consequence. The salutation predicts velocity and pressure fields of the non-Newtonian incompressible fluid filtration for conditions of a non-deformable formation as well as a gel front trajectory in the fracture. The mathematical model of agent injection into the main fracture is based on the fundamental laws of continuum mechanics conservation describing the flow of non-Newtonian and Newtonian fluids separated by an interface plane in a flat channel with permeable walls. The mathematical model is based on a one-dimensional isothermal approximation, with dynamic parameters pressure and velocity, averaged over the fracture section.

Although deployed in the vasculature to expand vessel diameter and improve blood flow, protruding stent struts can create complex flow environments associated with flow separation and oscillating shear gradients. Given the association between magnitude and direction of wall shear stress (WSS) and endothelial phenotype expression, accurate representation of stent-induced flow patterns is critical if we are to predict sites susceptible to intimal hyperplasia. Despite the number of stents approved for clinical use, quantification on the alteration of hemodynamic flow parameters associated with the Gianturco Z-stent is limited in the literature. In using experimental and computational models to quantify strut-induced flow, the majority of past work has assumed blood or representative analogs to behave as Newtonian fluids. However, recent studies have challenged the validity of this assumption. We present here the experimental quantification of flow through a Gianturco Z-stent wire in representative Newtonian and non-Newtonian blood analog environments using particle image velocimetry (PIV). Fluid analogs were circulated through a closed flow loop at physiologically appropriate flow rates whereupon PIV snapshots were acquired downstream of the wire housed in an acrylic tube with a diameter characteristic of the carotid artery. Hemodynamic parameters including WSS, oscillatory shear index (OSI), and Reynolds shear stresses (RSS) were measured. Our findings show that the introduction of the stent wire altered downstream hemodynamic parameters through a reduction in WSS and increases in OSI and RSS from nonstented flow. The Newtonian analog solution of glycerol and water underestimated WSS while increasing the spatial coverage of flow reversal and oscillatory shear compared to a non-Newtonianfluid of glycerol, water, and xanthan gum. Peak RSS were increased with the Newtonian fluid, although peak values were similar upon a doubling of flow rate. The introduction of the

Fluid mechanics of non-Newtonianfluids, which arise in numerous settings, are characterized by non-linear constitutive models that pose certain unique challenges for computational methods. Here, we consider the lattice Boltzmann method (LBM), which offers some computational advantages due to its kinetic basis and its simpler stream-and-collide procedure enabling efficient simulations. However, further improvements are necessary to improve its numerical stability and accuracy for computations involving broader parameter ranges. Hence, in this study, we extend the cascaded LBM formulation by modifying its moment equilibria and relaxation parameters to handle a variety of non-Newtonian constitutive equations, including power-law and Bingham fluids, with improved stability. In addition, we include corrections to the moment equilibria to obtain an inertial frame invariant scheme without cubic-velocity defects. After preforming its validation study for various benchmark flows, we study the physics of non-Newtonian flow over pairs of circular and square cylinders in a tandem arrangement, especially the wake structure interactions and their effects on resulting forces in each cylinder, and elucidate the effect of the various characteristic parameters.

According to the experimental work of C. Barus in Am. J. Sci. 45, 87 (1893), the dependency of liquid viscosity on pressure is exponential. Therefore, we extend the study of squeeze film problems of long partial journal bearings for Stokes non-Newtonian couple stress fluids by considering the pressure-dependent viscosity in the present paper. Through a small perturbation technique, we derive a first-order closed-form solution for the film pressure, the load capacity, and the response time of partial-bearing squeeze films. It is also found that the non-Newtonian couple-stress partial bearings with pressure-dependent viscosity provide better squeeze-film characteristics than those of the bearing with constant-viscosity situation. (orig.)

According to the experimental work of C. Barus in Am. J. Sci. 45, 87 (1893) [1], the dependency of liquid viscosity on pressure is exponential. Therefore, we extend the study of squeeze film problems of long partial journal bearings for Stokes non-Newtonian couple stress fluids by considering the pressure-dependent viscosity in the present paper. Through a small perturbation technique, we derive a first-order closed-form solution for the film pressure, the load capacity, and the response time of partial-bearing squeeze films. It is also found that the non-Newtonian couple-stress partial bearings with pressure-dependent viscosity provide better squeeze-film characteristics than those of the bearing with constant-viscosity situation.

In this paper, natural convection of non-Newtonian bio-nanofluids flow between two vertical flat plates is investigated numerically. Sodium Alginate (SA) and Sodium Carboxymethyl Cellulose (SCMC) are considered as the base non-Newtonianfluid, and nanoparticles such as Titania ( TiO2 and Alumina ( Al2O3 were added to them. The effective thermal conductivity and viscosity of nanofluids are calculated through Maxwell-Garnetts (MG) and Brinkman models, respectively. A fourth-order Runge-Kutta numerical method (NUM) and three Weighted Residual Methods (WRMs), Collocation (CM), Galerkin (GM) and Least-Square Method (LSM) and Finite-Element Method (FEM), are used to solve the present problem. The influence of some physical parameters such as nanofluid volume friction on non-dimensional velocity and temperature profiles are discussed. The results show that SCMC- TiO2 has higher velocity and temperature values than other nanofluid structures.

In the present work the momentum transport in two adjacent flow regions is described by means of a continuum theory of mixtures, specially developed to model multiphase phenomena. A generalized Newtonian fluid flows through the permeable wall channel, originating a pure fluid region and a mixture region - where the fluid saturates the porous matrix. The fluid and the porous matrix are treated as continuous constituents of a binary mixture coexisting superposed, each of them occupying simultaneously the whole volume of the mixture. An Ostwald-de Waele behavior is assumed for both the fluid constituent (in the mixture region) and the fluid (in the so-called pure fluid region), while the porous matrix, represented by the solid constituent, is assumed rigid, homogeneous, isotropic and at rest. Compatibility conditions at the interface (pure fluid-mixture) for momentum transfer are proposed and discussed. Assuming no flow across the interface, the velocity should be zero on the solid parts of the boundary and should match the fluid diffusing velocity on the fluid parts of the boundary. Also the shear stress at the pure fluid region is to be balanced by a multiple of the partial shear stress at the mixture region. A minimum principle for the above-described problem, assuming fully developed flow in both regions, is presented, providing an easy and reliable way for carrying out numerical simulations. (author)

An analysis is carried out to study the steady flow and heat transfer characteristics from a continuous flat surface moving in a parallel free stream of an electrically conducting non-Newtonian viscoelastic fluid. The flow is subjected to a transverse uniform magnetic field. The constitutive equation of the fluid is modeled by that for a second grade fluid. Numerical results are obtained for the distribution of velocity and temperature profiles. The effects of various physical parameters like viscoelastic parameter, magnetic parameter and Prandtl number on various momentum and heat transfer characteristics are discussed in detail and shown graphically.

The impact of non-Newtonian behavior and the dynamic contact angle on the rise dynamics of a power law liquid in a vertical capillary is studied theoretically and experimentally for quasi-steady-state flow. An analytical solution for the time evolution of the meniscus height is obtained in terms of a Gaussian hypergeometric function, which in the case of a Newtonian liquid reduces to the Lucas-Washburn equation modified by the dynamic contact angle correction. The validity of the solution is checked against experimental data on the rise dynamics of a shear-thinning cmc solution in a glass microcapillary, and excellent agreement is found.

By considering an ion moving inside an imaginary sphere filled with a power-law fluid, we bring out the implications of the fluid rheology and the influence of the proximity of the other ions towards evaluating the conduction current in an ionic solution. We show that the variation of the conductivity as a function of the ionic concentration is both qualitatively and quantitatively similar to that predicted by the Kohlrausch law. We then utilize this consideration for estimating streaming potentials developed across narrow fluidic confinements as a consequence of the transport of ions in a convective medium constituting a power-law fluid. These estimates turn out to be in sharp contrast to the classical estimates of streaming potential for non-Newtonianfluids, in which the effect of rheology of the solvent is merely considered to affect the advection current, disregarding its contributions to the conduction current. Our results have potential implications of devising a new paradigm of consistent estimation of streaming potentials for non-Newtonianfluids, with combined considerations of the confinement effect and fluid rheology in the theoretical calculations.

Pure separation and sorting of microparticles from complex fluids are essential for biochemical analyses and clinical diagnostics. However, conventional techniques require highly complex and expensive labeling processes for high purity separation. In this study, we present a simple and label-free method for separating microparticles with high purity using the elasto-inertial characteristic of a non-Newtonianfluid in microchannel flow. At the inlet, particle-containing sample flow was pushed toward the side walls by introducing sheath fluid from the center inlet. Particles of 1 μm and 5 μm in diameter, which were suspended in viscoelastic fluid, were successfully separated in the outlet channels: larger particles were notably focused on the centerline of the channel at the outlet, while smaller particles continued flowing along the side walls with minimal lateral migration towards the centerline. The same technique was further applied to separate platelets from diluted whole blood. Through cytometric analysis, we obtained a purity of collected platelets of close to 99.9%. Conclusively, our microparticle separation technique using elasto-inertial forces in non-Newtonianfluid is an effective method for separating and collecting microparticles on the basis of size differences with high purity.

Hydrodynamic and gas-liquid mass transfer characteristics, such as liquid velocity, gas holdup, solid holdup and gas-liquid volumetric mass transfer coefficient, in the riser and downcomer of the gas-liquid-solid three-phase internal loop airlift bioreactors with complete gas recirculation for non-Newtonianfluids, were investigated. A mathematical model for the description of flow behavior and gas-liquid mass transfer of these bioreactors was developed. The predicted results of this model agreed well with the experimental data.

This communication deals with the properties of heat source/sink in a magneto-hydrodynamic flow of a non-Newtonianfluid immersed in a porous medium. Shrinking phenomenon along with the permeability of the wall is considered. Mathematical modelling is performed to convert the considered physical process into set of coupled nonlinear mathematical equations. Suitable transformations are invoked to convert the set of partial differential equations into nonlinear ordinary differential equations which are tackled numerically for the solution computations. It is noted that dual solutions for various physical parameters exist which are analyzed in detail.

This paper studies mixed convection,double dispersion and chemical reaction effects on heat and mass transfer in a non-Darcy non-Newtonianfluid over a vertical surface in a porous medium under the constant temperature and concentration.The governing boundary layer equations,namely,momentum,energy and concentration,are converted to ordinary differential equations by introducing similarity variables and then are solved numerically by means of fourth-order Runge-Kutta method coupled with double-shooting techn...

An investigation is made of the magnetic Rayleigh problem where a semi-infinite plate is given an impulsive motion and thereafter moves with constant velocity in a nonNewtonian power law fluid of infinite extent. The solution of this highly non-linear problem is obtained by means of the transformation group theoretic approach. The one-parameter group transformation reduces the number of independent variables by one and the governing partial differential equation with the boundary conditions reduce to an ordinary differential equation with the appropriate boundary conditions. Effect of the some parameters on the velocity u ( y, t) has been studied and the results are plotted.

Full Text Available In this contribution a numerical study is carried out to analyze the effect of slip at the boundary of unsteady two-dimensional MHD flow of a non-Newtonianfluid over a stretching surface having a prescribed surface temperature in the presence of suction or blowing at the surface. Casson fluid model is used to characterize the non-Newtonianfluid behavior. With the help of similarity transformations, the governing partial differential equations corresponding to the momentum and heat transfer are reduced to a set of non-linear ordinary differential equations, which are then solved for local similar solutions using the very robust computer algebra software MATLAB. The flow features and heat transfer characteristics for different values of the governing parameters are graphically presented and discussed in detail. Comparison with available results for certain cases is excellent. The effect of increasing values of the Casson parameter is seen to suppress the velocity field. But the temperature is enhanced with increasing Casson parameter. For increasing slip parameter, velocity increases and thermal boundary layer becomes thinner in the case of suction or blowing.

In the current study, a direct-forcing immersed boundary-non-Newtonian lattice Boltzmann method (IB-NLBM) is developed to investigate the sedimentation and interaction of particles in shear-thinning and shear-thickening fluids. In the proposed IB-NLBM, the non-linear mechanics of non-Newtonian particulate flows is detected by combination of the most desirable features of immersed boundary and lattice Boltzmann methods. The noticeable roles of non-Newtonian behavior on particle motion, settling velocity and generalized Reynolds number are investigated by simulating benchmark problem of one-particle sedimentation under the same generalized Archimedes number. The effects of extra force due to added accelerated mass are analyzed on the particle motion which have a significant impact on shear-thinning fluids. For the first time, the phenomena of interaction among the particles, such as Drafting, Kissing, and Tumbling in non-Newtonianfluids are investigated by simulation of two-particle sedimentation and twelve-particle sedimentation. The results show that increasing the shear-thickening behavior of fluid leads to a significant increase in the kissing time. Moreover, the transverse position of particles for shear-thinning fluids during the tumbling interval is different from Newtonian and the shear-thickening fluids. The present non-Newtonian particulate study can be applied in several industrial and scientific applications, like the non-Newtonian sedimentation behavior of particles in food industrial and biological fluids.

In this work the instability of the Taylor-Couette flow for Newtonian and non-Newtonianfluids (dilatant and pseudoplastic fluids) is investigated for cases of finite aspect ratios. The study is conducted numerically using the lattice Boltzmann method (LBM). In many industrial applications, the apparatuses and installations drift away from the idealized case of an annulus of infinite length, and thus the end caps effect can no longer be ignored. The inner cylinder is rotating while the outer one and the end walls are maintained at rest. The lattice two-dimensional nine-velocity (D2Q9) Boltzmann model developed from the Bhatnagar-Gross-Krook approximation is used to obtain the flow field for fluids obeying the power-law model. The combined effects of the Reynolds number, the radius ratio, and the power-law index n on the flow characteristics are analyzed for an annular space of finite aspect ratio. Two flow modes are obtained: a primary Couette flow (CF) mode and a secondary Taylor vortex flow (TVF) mode. The flow structures so obtained are different from one mode to another. The critical Reynolds number Re(c) for the passage from the primary to the secondary mode exhibits the lowest value for the pseudoplastic fluids and the highest value for the dilatant fluids. The findings are useful for studies of the swirling flow of non-Newtoniansfluids in axisymmetric geometries using LBM. The flow changes from the CF to TVF and its structure switches from the two-cells to four-cells regime for both Newtonian and dilatant fluids. Contrariwise for pseudoplastic fluids, the flow exhibits 2-4-2 structure passing from two-cells to four cells and switches again to the two-cells configuration. Furthermore, the critical Reynolds number presents a monotonic increase with the power-law index n of the non-Newtonianfluid, and as the radius ratio grows, the transition flow regimes tend to appear for higher critical Reynolds numbers.

This paper demonstrates magneto-hydrodynamic (MHD) mixed convection flow through a channel with a rectangular obstacle at the entrance region using non-Newtonian power law fluid. The obstacle is kept at uniformly high temperature whereas the inlet and top wall of the channel are maintained at a temperature lower than obstacle temperature. Poiseuille flow is implemented as the inlet velocity boundary condition. Grid independency test and code validation are performed to justify the computational accuracy before solving the present problem. Galerkin weighted residual method has been appointed to solve the continuity, momentum and energy equations. The problem has been solved for wide range of pertinent parameters like Richardson number (Ri = 0.1 - 10) at a constant Reynolds number (Re = 100), Hartmann number (Ha = 0 - 100), power index (n = 0.6 - 1.6). The flow and thermal field have been thoroughly discussed through streamline and isothermal lines respectively. The heat transfer performance of the given study has been illustrated by average Nusselt number plots. It is observed that increment of Hartmann number (Ha) tends to decrease the heat transfer rate up to a critical value (Ha = 20) and then let increase the heat transfer performance. Thus maximum heat transfer rate has been recorded for higher Hartmann number and Rayleigh number in case of pseudo-plastic (n = 0.6) non-Newtonianfluid flow.

Full Text Available In the present study, the effect of viscous dissipation on magnetohydrodynamic (MHD non-Darcian free-convection flow of a non-Newtonian power-law fluid past a vertical flat plate in a saturated porous medium with variable viscosity and temperature jump is considered. The fluid is permeated by a transverse magnetic field imposed perpendicularly to the plate on the assumption of a small magnetic Reynolds number. The fluid viscosity is assumed to vary as a reciprocal of linear function of temperature. The governing boundary layer equations and boundary conditions are cast into a dimensionless form and simplified by using a similarity transformation into a system of nonlinear ordinary differential equations and solved numerically. The effects of the governing parameters on the flow fields and heat transfer are shown in graphs and tabular form.

The Rayleigh-Bénard convection for non-Newtonianfluids possessing both viscoelastic and shear-thinning behaviours is examined. The Phan-Thien-Tanner (PTT) constitutive equation is implemented to model the non-Newtonian character of the fluid. It is found that while the shear-thinning and viscoelastic effects could annihilate one another for the steady roll flow, presence of both behaviours restricts the roll stability limit significantly compared to the cases when the fluid is either inelastic shear-thinning or purely viscoelastic with constant viscosity.

Full Text Available Due to increased production of heavy and extra heavy crude in Mexico, it has led to the necessity touse chemicals to facilitate the transport in the pipe of our country. Experimental study was conductedto analyze the influence of a viscosity reducer of biological origin (BRV, on the rheological behaviorof heavy oil in the northern region of Mexico, finding that it exhibits a non-Newtonian viscoelasticbehavior, where a concentration increase of BRV leads to a consistency decrease and an increasedflow order, where dilatant behavior was observed in high temperatures. From these results it wasestimated the pressure losses by friction in a horizontal pipe for single phase and two phase flow. Wefound that in all cases the increase in the concentration of BRV reduces these losses.

In this work, the long-term stability of titanium oxide nanowire suspensions was accessed by an accelerated sedimentation with centrifugal forces. Titanium oxide (TiO2) nanoparticle (NP) and nanowire (NW) dispersions were prepared, and their sizes were carefully characterized. To replace the time-consuming visual observation, sedimentation velocities of the TiO2 NP and NW suspensions were measured using an analytical centrifuge. For an aqueous TiO2 NP suspension, the measured sedimentation velocities were linearly dependent on the relative centrifugal forces (RCF), as predicted by the classical Stokes law. A similar linear relationship was also found in the case of TiO2 NW aqueous suspensions. However, NWs preferred to settle parallel to the centrifugal direction under high RCF because of the lower flow resistance along the long axis. Thus, the extrapolated sedimentation velocity under regular gravity can be overestimated. Finally, a stable TiO2 NW suspension was formulated with a shear thinning fluid and showed great stability for weeks using visual observation. A theoretical analysis was deduced with rheological shear-thinning parameters to describe the nonlinear power-law dependence between the measured sedimentation velocities and RCF. The good agreement between the theoretical predictions and measurements suggested that the sedimentation velocity can be properly extrapolated to regular gravity. In summary, this accelerated assessment on a theoretical basis can yield quantitative information about long-term stability within a short time (a few hours) and can be further extended to other suspension systems.

. In this context it is natural to look for other sources of non-linearity and one possibility is to introduce a non-Newtonian working fluid. Non-Newtonian properties are due to stretching of large particles/molecules in the fluid and this is commonly seen for biological samples in “lab-on-a-chip” systems....... The strength of non-Newtonian effects does not depend on the device size. Furthermore a non-Newtonian working fluid removes symmetry properties such that geometry influence is reintroduced, and indeed non-Newtonian effects have been used in experimentally realized microfluidic rectitifiers[1]. The rectifiers...... optimization, which is a kind of design optimization where nothing is assumed about the topology of the design. We will apply a high-level implementation of topology optimization using the density method in a commercial finite element package[2]. However, the modeling of non-Newtonianfluids remains a major...

In this study, we investigated inelastic non-Newtonianfluid flow over heterogeneously slippery surfaces. First, we simulated the flow of aqueous xanthan gum solutions over a bubble mattress, which is a superhydrophobic surface consisting of transversely positioned no-slip walls and no-shear gas bub

The convective heat transfer, friction, and rheological properties of various types of nonNewtonianfluid in circular tube flows were investigated. If an apparent Reynolds number is used and if the temperature and degradation effects are properly taken into account, the reduced turbulent friction and heat transfer results, respectively, are then shown to be well correlated by the same expressions for different fluids, regardless of the nature of the fluids and whether they are shear-thinning or shear-thickening. This representation can also separate the reductions in turbulent heat transfer and friction that are induced by viscoelasticity from those induced by pseudoplasticity. Polyacrylamide solutions inducing asymptotic and intermediate drag reduction regimes were investigated over a broad range of Reynolds numbers. A kerosene-based antimisting polymer solution was also studied. Suspensions of bentonite of various concentrations were investigated in laminar and turbulent regimes, and the results for fully developed and entrance flows were well correlated by Newtonian relationships when an adequate wall viscosity concept was used.

Many industrial flow processes are sensitive to changes in the rheological behaviour of process fluids, and there therefore exists a need for methods that provide online, or inline, rheological characterisation necessary for process control and optimisation over timescales of minutes or less. Nuclear magnetic resonance (NMR) offers a non-invasive technique for this application, without limitation on optical opacity. We present a Bayesian analysis approach using pulsed field gradient (PFG) NMR to enable estimation of the rheological parameters of Herschel-Bulkley fluids in a pipe flow geometry, characterised by a flow behaviour index n , yield stress τ0 , and consistency factor k , by analysis of the signal in q -space. This approach eliminates the need for velocity image acquisition and expensive gradient hardware. We investigate the robustness of the proposed Bayesian NMR approach to noisy data and reduced sampling using simulated NMR data and show that even with a signal-to-noise ratio (SNR) of 100, only 16 points are required to be sampled to provide rheological parameters accurate to within 2% of the ground truth. Experimental validation is provided through an experimental case study on Carbopol 940 solutions (model Herschel-Bulkley fluids) using PFG NMR at a 1H resonance frequency of 85.2 MHz; for SNR > 1000, only 8 points are required to be sampled. This corresponds to a total acquisition time of non-Bayesian NMR methods demonstrates that the Bayesian NMR approach is in agreement with MR flow imaging to within the accuracy of the measurement. Furthermore, as we increase the concentration of Carbopol 940 we observe a change in rheological characteristics, probably due to shear history-dependent behaviour and the different geometries used. This behaviour highlights the need for online, or inline, rheological characterisation in industrial process applications.

Full Text Available This paper is devoted to the study of the peristaltic motion of non-Newtonianfluid with heat and mass transfer through a porous medium in the channel under the effect of magnetic field. A modified Casson non-Newtonian constitutive model is employed for the transport fluid. A perturbation series’ method of solution of the stream function is discussed. The effects of various parameters of interest such as the magnetic parameter, Casson parameter, and permeability parameter on the velocity, pressure rise, temperature, and concentration are discussed and illustrated graphically through a set of figures.

The problem of thermal dispersion effects on unsteady free convection from an isothermal horizontal circular cylinder to a non-Newtonianfluid saturating a porous medium is examined numerically. The Darcy-Brinkman-Forchheimer model is employed to describe the flow field. The thermal diffusivity coefficient has been assumed to be the sum of the molecular diffusivity and the dynamic diffusivity due to mechanical dispersion. The simultaneous development of the momentum and thermal boundary layers are obtained by using finite difference method. The stability conditions are determined for each difference equation. Using an explicit finite difference scheme, solutions at each time-step have been found and then stepped forward in time until reaching steady state solution. Velocity and temperature profiles are shown graphically. It is found that as time approaches infinity, the values of friction factor and heat transfer coefficient approach the steady state values.

Liquids to be broken up using a prefilming airblast atomizer are usually Newton liquids with relatively low viscosities. While in some industrial processes, such as spray drying, liquids to be atomized are high concentration suspensions or non-Newtonianfluids with high viscosities. In this paper, non-Newtonianfluids with viscosity up to 4. 4 Pa · s were effectively atomized using a specially designed prefilming airblast atomizer. The atomizer enabled liquid to extend to a thickness-adjustable film and forced the atomizing air stream to swirl with 30° or 45° through gas distributors with spiral slots. The liquid film was impinged by the swirling air stream resulting in the disintegration of the film into drops. Drop sizes were measured using a laser diffraction technique.An improved four-parameter mathematical model was established to relate the Sauter mean diameter of drops to the atomization conditions in terms of power dependencies on three dimensionless groups: Weber number,Ohnesorge number and air liquid mass ratio. The friction on the surface of the 1iquid film made by swirling air stream played an important role in the prefilming atomization at the conditions of low air velocity and low liquid viscosity. In this case, the liquid film was disintegrated into drops according to the classical wavy-sheet mechanism, thus thinner liquid films and high swirl levels of the atomizing air produced smaller drops. With the increase of the air velocity and the liquid viscosity, the effect of the friction on the prefilming atomization relatively weakened, whereas the impingement on the liquid film made by atomizing air stream in a direction normal to the liquid film and corresponding momentum transfer gradually strengthened and eventually dominated the disruption of liquid into drops, which induced that the initial thickness of the liquid film and the swirl of atomizing air stream exercised a minor influence on the drop sizes.

A numerical simulation to investigate the Non-Newtonian modelling effects on physiological flows in a three dimensional idealized artery with a single stenosis of 85% severity. The wall vessel is considered to be rigid. Oscillatory physiological and parabolic velocity profile has been imposed for inlet boundary condition. Where the physiological waveform is performed using a Fourier series with sixteen harmonics. The investigation has a Reynolds number range of 96 to 800. Low Reynolds number k - ω model is used as governing equation. The investigation has been carried out to characterize two Non-Newtonian constitutive equations of blood, namely, (i) Carreau and (ii) Cross models. The Newtonian model has also been investigated to study the physics of fluid. The results of Newtonian model are compared with the Non-Newtonian models. The numerical results are presented in terms of pressure, wall shear stress distributions and the streamlines contours. At early systole pressure differences between Newtonian and Non-Newtonian models are observed at pre-stenotic, throat and immediately after throat regions. In the case of wall shear stress, some differences between Newtonian and Non-Newtonian models are observed when the flows are minimum such as at early systole or diastole.

Mass transfer rates were measured in a large scale system, which consisted of an 8.4 meter tall by 0.76 meter diameter column containing one of three fluids: water with an anti-foam agent, water without an anti-foam agent, and AZ101 simulant, which simulated a non-Newtonian nuclear waste. The testing contributed to the evaluation of large scale mass transfer of hydrogen in nuclear waste tanks. Due to its radioactivity, the waste was chemically simulated, and due to flammability concerns oxygen was used in lieu of hydrogen. Different liquids were used to better understand the mass transfer processes, where each of the fluids was saturated with oxygen, and the oxygen was then removed from solution as air bubbled up, or sparged, through the solution from the bottom of the column. Air sparging was supplied by a single tube which was co-axial to the column, the decrease in oxygen concentration was recorded, and oxygen measurements were then used to determine the mass transfer coefficients to describe the rate of oxygen transfer from solution. Superficial, average, sparging velocities of 2, 5, and 10 mm/second were applied to each of the liquids at three different column fill levels, and mass transfer coefficient test results are presented here for combinations of superficial velocities and fluid levels.

A theoretical and experimental analysis of non-Newtonian gravity-driven flow in porous media with spatially variable properties is presented. The motivation for our study is the rheological complexity exhibited by several environmental contaminants (wastewater sludge, oil pollutants, waste produced by the minerals and coal industries) and remediation agents (suspensions employed to enhance the efficiency of in-situ remediation). Natural porous media are inherently heterogeneous, and this heterogeneity influences the extent and shape of the porous domain invaded by the contaminant or remediation agent. To grasp the combined effect of rheology and spatial heterogeneity, we consider: a) the release of a thin current of non-Newtonian power-law fluid into a 2-D, semi-infinite and saturated porous medium above a horizontal bed; b) perfectly stratified media, with permeability and porosity varying along the direction transverse (vertical) or parallel (horizontal) to the flow direction. This continuous variation of spatial properties is described by two additional parameters. In order to represent several possible spreading scenarios, we consider: i) instantaneous injection with constant mass; ii) continuous injection with time-variable mass; iii) instantaneous release of a mound of fluid, which can drain freely out of the formation at the origin (dipole flow). Under these assumptions, scalings for current length and thickness are derived in self similar form. An analysis of the conditions on model parameters required to avoid an unphysical or asymptotically invalid result is presented. Theoretical results are validated against multiple sets of experiments, conducted for different combinations of spreading scenarios and types of stratification. Two basic setups are employed for the experiments: I) direct flow simulation in an artificial porous medium constructed superimposing layers of glass beads of different diameter; II) a Hele-Shaw (HS) analogue made of two parallel

Full Text Available The purpose of this article is to study and analyze the convective flow of a third grade non-Newtonianfluid due to a linearly stretching sheet subject to a magnetic field. The dimensionless entropy generation equation is obtained by solving the reduced momentum and energy equations. The momentum and energy equations are reduced to a system of ordinary differential equations by a similarity method. The optimal homotopy analysis method (OHAM is used to solve the resulting system of ordinary differential equations. The effects of the magnetic field, Biot number and Prandtl number on the velocity component and temperature are studied. The results show that the thermal boundary-layer thickness gets decreased with increasing the Prandtl number. In addition, Brownian motion plays an important role to improve thermal conductivity of the fluid. The main purpose of the paper is to study the effects of Reynolds number, dimensionless temperature difference, Brinkman number, Hartmann number and other physical parameters on the entropy generation. These results are analyzed and discussed.

L-Arginine is an important component of amino acid injection. Its diffusion in body fluid and blood is of key importance to understand drug diffusion and drug release. As a fundamental demand for study and being a considerably valuable reference for application, in this study, the diffusion coefficients of L-arginine in polyacryla-mide(PAM) aqueous solution used as non-Newtonianfluid similar to blood and body fluid were measured using a holographic interferometer. The effects of interaction among molecules and solution concentration on diffusion were analyzed and discussed, respectively. Based on the obstruction-scaling model, a novel modified model was presented for predicting diffusivity of solute in non-Newtonianfluid. Good agreement was achieved between the calculated value and the experimental data.

A study is presented for magnetohydrodynamics (MHD) flow and heat trans-fer characteristics of a viscous incompressible electrically conducting micropolar fluid in a channel with stretching walls. The micropolar model introduced by Eringen is used to describe the working fluid. The transformed self similar ordinary differential equations together with the associated boundary conditions are solved numerically by an algorithm based on quasi-linearization and multilevel discretization. The effects of some physical parameters on the flow and heat transfer are discussed and presented through tables and graphs. The present investigations may be beneficial in the flow and thermal control of polymeric processing.

A comprehensive modeling of landslide generated waves using an in-house parallel Incompressible Smoothed Particle Hydrodynamics (ISPH) code is presented in this paper. The study of landslide generated waves is challenging due to the involvement of several complex physical phenomena, such as slide-water interaction, turbulence and complex free surface profiles. A numerical tool that can efficiently calculate both slide motion, impact with the surface and the resulting wave is needed for ongoing study of these phenomena. Mesh-less numerical methods, such as Smoothed Particle Hydrodynamics (SPH), handle the slide motion and the complex free surface profile with ease. In this paper, an in-house parallel explicit ISPH code is used to simulate both subaerial and submarine landslides in 2D and in more realistic 3D applications. Both rigid and deformable slides are used to generate the impulsive waves. A landslide case is simulated where a slide falls into a non-Newtonian reservoir fluid (water-bentonite mixture). A new technique is also proposed to calculate the motion of a rigid slide on an inclined ramp implicitly, without using the prescribed motion in SPH. For all the test cases, results generated from the proposed ISPH method are compared with available experimental data and show good agreement.

Full Text Available A large number of chemical operations, biochemical or petrochemical industry is very depending on the rheological fluids nature. In this work, we study the case of highly viscous of viscoplastic fluids in a classical system of agitation: a cylindrical tank with plate bottom without obstacles agitated by gate impeller agitator. We are interested to the laminar, incompressible and isothermal flows. We devote to a numerical approach carried out using an industrial code CFD Fluent 6.3.26 based on the method of finites volumes discretization of Navier - Stokes equations formulated in variables (U.V.P. The threshold of flow related to the viscoplastic behavior is modeled by a theoretical law of Bingham. The results obtained are used to compare between the five configurations suggested of power consumption. We study the influence of inertia by the variation of Reynolds number.

The present investigation deals with finding the trajectories of the drug dosed magnetic carrier particle in a microvessel with two-phase fluid model which is subjected to the external magnetic field. The radius of the microvessel is divided into the endothelial glycocalyx layer in which the blood is assumed to obey Newtonian character and a core and plug regions where the blood obeys the non-Newtonian Herschel-Bulkley character which is suitable for the microvessel of radius 50 microm. The carrier particles, bound with nanoparticles and drug molecules are injected into the vascular system upstream from malignant tissue, and captured at the tumor site using a local applied magnetic field. The applied magnetic field is produced by a cylindrical magnet positioned outside the body and near the tumor position. The expressions for the fluidic force for the carrier particle traversing in the two-phase fluid in the microvessel and the magnetic force due to the external magnetic field are obtained. Several factors that influence the magnetic targeting of the carrier particles in the microvasculature, such as the size of the carrier particle, the volume fraction of embedded magnetic nanoparticles, and the distance of separation of the magnet from the axis of the microvessel are considered in the present problem. An algorithm is given to solve the system of coupled equations for trajectories of the carrier particle in the invasive case. The trajectories of the carrier particle are found for both invasive and noninvasive targeting systems. A comparison is made between the trajectories in these cases. Also, the present results are compared with the data available for the impermeable microvessel with single-phase fluid flow. Also, a prediction of the capture of therapeutic magnetic nanoparticle in the impermeable microvasculature is made for different radii, distances and volume fractions in both the invasive and noninvasive cases.

In this work, a new mathematical model of thermoelectric MHD theory has been constructed in the context of a new consideration of heat conduction with fractional order. This model is applied to Stokes' first problem for a viscoelastic fluid with heat sources. Laplace transforms and state-space techniques will be used to obtain the general solution for any set of boundary conditions. According to the numerical results and its graphs, conclusion about the new theory has been constructed. Some comparisons have been shown in figures to estimate the effects of the fractional order parameter on all the studied fields.

Many microorganisms find themselves immersed in fluids displaying non-Newtonian rheological properties such as viscoelasticity and shear-thinning viscosity. The effects of viscoelasticity on swimming at low Reynolds numbers have already received considerable attention, but much less is known about swimming in shear-thinning fluids. A general understanding of the fundamental question of how shear-thinning rheology influences swimming still remains elusive. To probe this question further, we study a spherical squirmer in a shear-thinning fluid using a combination of asymptotic analysis and numerical simulations. Shear-thinning rheology is found to affect a squirming swimmer in nontrivial and surprising ways; we predict and show instances of both faster and slower swimming depending on the surface actuation of the squirmer. We also illustrate that while a drag and thrust decomposition can provide insights into swimming in Newtonian fluids, extending this intuition to problems in complex media can prove problemat...

The hear transfer mechanism and the constitutive models for energy boundary layer in power law fluids were investigated.Two energy transfer constitutive equations models were proposed based on the assumption of similarity of velocity field momentum diffusion and temperature field heat transfer.The governing systems of partial different equations were transformed into ordinary differential equations respectively by using the similarity transformation group.One model was assumed that Prandtl number is a constant,and the other model was assumed that viscosity diffusion is analogous to thermal diffusion.The solutions were presented analytically and numerically by using the Runge-Kutta formulas and shooting technique and the associated transfer characteristics were discussed.

Many applications of twin-screw extruders are found in the processing of food, plastics, pharmaceutical materials and other highly viscous materials. In reactive extrusion, complex interactions in which the flow pattern, and the heat and mass transfer are affected by viscous dissipation, reaction energy, convection, residence time distribution and rheology of the materials may occur. The fluid flow, heat transfer and chemical reactions in a fully intermeshing, corotating and self wiping twin screw extruder were investigated numerically by using the finite volume method. The screw channel of a twin screw extruder are approximated as translation (parabolic) domain and intermeshing (elliptic) domain. The full governing equations were solved to determine the velocity components in the three coordinate directions. The energy equation is coupled with the equations of motion through viscosity. The Residence Time Distribution (RTD), was obtained by using a particle tracking method. The flow field, temperature field, pressure as well as RTD and chemical conversion were obtained by numerical simulation and the results yielded agreement with experimental measurements and expected physical characteristic of the process.

A small scale isotropic mass transfer model was developed for the local liquid side mass transfer coefficients in gas-liquid-solid three-phase flow airlift loop reactor for Newtonian and non-Newtonianfluids. It is based on Higbie's penetration theory and Kolmogoroff's theory of isotropic turbulence with kl=3√2D∈11/3/π(η1-1/3-λf-1/3)where e1 is local rate of energy dissipation, Af is the local microscale, r/l is the local Kolmogoroff scale and D is the diffusion coefficient. The capability of the proposed model is discussed in the light of experimental data obtained from 12 L gas-liquid-solid three-phase flow airlift loop reactor using Newtonian and non-Newtonianfluids. Good agreement with the experimental data was obtained over a wide range of conditions suggesting a general applicability of the proposed model.

While significant research has been dedicated to the simulation of fluids, not much attention has been given to exploring new interesting behavior that can be generated with the different types of non-Newtonianfluids with non-constant viscosity. Going in this direction, this paper introduces a computational model for simulating the interesting phenomena observed in non-Newtonianshear thickening fluids, which are fluids where the viscosity increases with increased stress. These fluids have unique and unconventional behavior, and they often appear in real world scenarios such as when sinking in quicksand or when experimenting with popular cornstarch and water mixtures. While interesting behavior of shear thickening fluids can be easily observed in the real world, the most interesting phenomena of these fluids have not been simulated before in computer graphics. The fluid exhibits unique phase changes between solid and liquid states, great impact resistance in its solid state and strong hysteresis effects. Our...

Full Text Available Helical flow in an annular space occurs during oil drilling operations. The correct prediction of flow of drilling fluid in an annular space between the wellbore wall and the drill pipe is essential to determine the variation in fluid pressure within the wellbore. This paper presents experimental and CFD simulation results of the pressure drop in the flow of non-Newtonianfluids through a concentric annular section and another section with fixed eccentricity (E = 0.75, using aqueous solutions of two distinct polymers (Xanthan Gum and Carboxymethylcellulose. The hydrodynamic behavior in this annular system was analyzed based on the experimental and CFD results, providing important information such as the formation of zones with preferential flows and stagnation regions.

There are many differences between the Newtonian fluid and the non-Newtonianfluid, and there is a few or even not teaching apparatus to demonstrate the behavior differences between the Newtonian fluid and the non-Newtonianfluid. To strengthen understanding of the Newtonian fluid and the non-Newtonianfluid, a teaching apparatus to demonstrate the velocity distribution differences in laminar flow between the Newtonian fluid and the non-Newtonianfluid was designed and made based on the flow characteristics differences. The movement behaviors of the Newtonian fluid and the non-Newtonianfluid were displayed by the tracer liquid developed by us. The velocity distribution differences at laminar flow between the Newtonian fluid and the non-Newtonianfluid can be found easily and directly in the demonstration apparatus.%牛顿流体和非牛顿流体存在着较大的差异，有关牛顿流体和非牛顿流体特性差异方面的教学演示仪器还较少，有些还处于空白。为了加强学生对牛顿流体和非牛顿流体的认识，本文根据牛顿流体与非牛顿流体流动特性差异，设计制作了表现牛顿流体和非牛顿流体层流流速分布差异的演示仪器;利用自行研制的示踪液体演示了非牛顿流体和牛顿流体运动过程，直观的展示了牛顿流体与非牛顿流体层流流速分布的差异。

This paper deals with some unsteady unidirectional transient flows of Oldroyd-B fluid in an annular pipe. The fractional calculus approach in the constitutive relationship model Oldroyd-B fluid is introduced and a generalized Jeffreys model with the fractional calculus has been built. Exact solutions of some unsteady flows of Oldroyd-B fluid in an annular pipe are obtained by using Hankel transform and Laplace transform for fractional calculus. The following four problems have been studied: (1) Poiseuille flow due to a constant pressure gradient; (2) axial Couette flow in an annulus; (3) axial Couette flow in an annulus due to a longitudinal constant shear; (4) Poiseuille flow due to a constant pressure gradient and a longitudinal constant shear. The well-known solutions for Navier-Stokes fluid, as well as those corresponding to a Maxwell fluid and a second grade one, appear as limited cases of our solutions.

This paper deals with some unsteady unidirectional transient flows of Oldroyd-B fluid in an annular pipe. The fractional calculus approach in the constitutive relationship model Oldroyd-B fluid is introduced and a generalized Jeffreys model with the fractional calculus has been built. Exact solutions of some unsteady flows of Oldroyd-B fluid in an annular pipe are obtained by using Hankel transform and Laplace transform for fractional calculus. The following four problems have been studied: (1) Poiseuille flow due to a constant pressure gradient; (2) axial Couette flow in an annulus; (3) axial Couette flow in an annulus due to a longitudinal constant shear; (4) Poiseuille flow due to a constant pressure gradient and a longitudinal constant shear. The well-known solutions for Navier-Stokes fluid, as well as those corresponding to a Maxwell fluid and a second grade one, appear as limited cases of our solutions.

This work focuses on the comparison between Newtonian and non-Newtonian blood flows through a bileaflet mechanical heart valve in the aortic root. The blood, in fact, is a concentrated suspension of cells, mainly red blood cells, in a Newtonian matrix, the plasma, and consequently its overall behavior is that of a non-Newtonianfluid owing to the action of the cells' membrane on the fluid part. The common practice, however, assumes the blood in large vessels as a Newtonian fluid since the shear rate is generally high and the effective viscosity becomes independent of the former. In this paper, we show that this is not always the case even in the aorta, the largest artery of the systemic circulation, owing to the pulsatile and transitional nature of the flow. Unexpectedly, for most of the pulsating cycle and in a large part of the fluid volume, the shear rate is smaller than the threshold level for the blood to display a constant effective viscosity and its shear thinning character might affect the system dynamics. A direct inspection of the various flow features has shown that the valve dynamics, the transvalvular pressure drop and the large-scale features of the flow are very similar for the Newtonian and non-Newtonianfluid models. On the other hand, the mechanical damage of the red blood cells (hemolysis), induced by the altered stress values in the flow, is larger for the non-Newtonianfluid model than for the Newtonian one.

The Department of Energy’s (DOE) National Energy Technology Laboratory (NETL) sponsored a workshop on non-Newtonian multiphase slurry at NETL’s Morgantown campus August 19 and 20, 2013. The objective of this special two-day meeting of 20-30 invited experts from industry, National Labs and academia was to identify and address technical issues associated with handling non-Newtonian multiphase slurries across various facilities managed by DOE. Particular emphasis during this workshop was placed on applications managed by the Office of Environmental Management (EM). The workshop was preceded by two webinars wherein personnel from ORP and NETL provided background information on the Hanford WTP project and discussed the critical design challenges facing this project. In non-Newtonianfluids, viscosity is not constant and exhibits a complex dependence on applied shear stress or deformation. Many applications under EM’s tank farm mission involve non-Newtonian slurries that are multiphase in nature; tank farm storage and handling, slurry transport, and mixing all involve multiphase flow dynamics, which require an improved understanding of the mechanisms responsible for rheological changes in non-Newtonian multiphase slurries (NNMS). To discuss the issues in predicting the behavior of NNMS, the workshop focused on two topic areas: (1) State-of-the-art in non-Newtonian Multiphase Slurry Flow, and (2) Scaling up with Confidence and Ensuring Safe and Reliable Long-Term Operation.

Development of many conditions and disorders, such as atherosclerosis and stroke, are dependent upon hemodynamic forces. To accurately predict and prevent these conditions and disorders hemodynamic forces must be properly mapped. Here we compare a shear-rate dependent fluid (SDF) constitutive model, based on the works by Yasuda et al in 1981, against a Newtonian model of blood. We verify our stabilized finite element numerical method with the benchmark lid-driven cavity flow problem. Numerical simulations show that the Newtonian model gives similar velocity profiles in the 2-dimensional cavity given different height and width dimensions, given the same Reynolds number. Conversely, the SDF model gave dissimilar velocity profiles, differing from the Newtonian velocity profiles by up to 25% in velocity magnitudes. This difference can affect estimation in platelet distribution within blood vessels or magnetic nanoparticle delivery. Wall shear stress (WSS) is an important quantity involved in vascular remodeling through integrin and adhesion molecule mechanotransduction. The SDF model gave a 7.3-fold greater WSS than the Newtonian model at the top of the 3-dimensional cavity. The SDF model gave a 37.7-fold greater WSS than the Newtonian model at artery walls located immediately after bifurcations in the idealized femoral artery tree. The pressure drop across arteries reveals arterial sections highly resistive to flow which correlates with stenosis formation. Numerical simulations give the pressure drop across the idealized femoral artery tree with the SDF model which is approximately 2.3-fold higher than with the Newtonian model. In atherosclerotic lesion models, the SDF model gives over 1 Pa higher WSS than the Newtonian model, a difference correlated with over twice as many adherent monocytes to endothelial cells from the Newtonian model compared to the SDF model.

Full Text Available Development of many conditions and disorders, such as atherosclerosis and stroke, are dependent upon hemodynamic forces. To accurately predict and prevent these conditions and disorders hemodynamic forces must be properly mapped. Here we compare a shear-rate dependent fluid (SDF constitutive model, based on the works by Yasuda et al in 1981, against a Newtonian model of blood. We verify our stabilized finite element numerical method with the benchmark lid-driven cavity flow problem. Numerical simulations show that the Newtonian model gives similar velocity profiles in the 2-dimensional cavity given different height and width dimensions, given the same Reynolds number. Conversely, the SDF model gave dissimilar velocity profiles, differing from the Newtonian velocity profiles by up to 25% in velocity magnitudes. This difference can affect estimation in platelet distribution within blood vessels or magnetic nanoparticle delivery. Wall shear stress (WSS is an important quantity involved in vascular remodeling through integrin and adhesion molecule mechanotransduction. The SDF model gave a 7.3-fold greater WSS than the Newtonian model at the top of the 3-dimensional cavity. The SDF model gave a 37.7-fold greater WSS than the Newtonian model at artery walls located immediately after bifurcations in the idealized femoral artery tree. The pressure drop across arteries reveals arterial sections highly resistive to flow which correlates with stenosis formation. Numerical simulations give the pressure drop across the idealized femoral artery tree with the SDF model which is approximately 2.3-fold higher than with the Newtonian model. In atherosclerotic lesion models, the SDF model gives over 1 Pa higher WSS than the Newtonian model, a difference correlated with over twice as many adherent monocytes to endothelial cells from the Newtonian model compared to the SDF model.

Full Text Available We analyzed in this paper the problem of mixed convection along a vertical plate in a non-Newtonianfluid saturated non-Darcy porous medium in the presence of melting and thermal dispersion-radiation effects for aiding and opposing external flows. Similarity solution for the governing equations is obtained for the flow equations in steady state. The equations are numerically solved by using Runge-kutta fourth order method coupled with shooting technique. The effects of melting (M, thermal dispersion (D, radiation (R, magnetic field (MH, viscosity index (n and mixed convection (Ra/Pe on fluid velocity and temperature are examined for aiding and opposing external flows.

Full Text Available The present article examines the flow, heat and mass transfer of a non-Newtonianfluid known as Casson fluid over a stretching surface in the presence of thermal radiations effects. Lie Group analysis is used to reduce the governing partial differential equations into non-linear ordinary differential equations. These equations are then solved by an analytical technique known as Homotopy Analysis Method (HAM. A comprehensive study of the problem is being made for various parameters involving in the equations through tables and graphs.

Full Text Available This paper investigates the MHD flow and heat transfer of an electrically conducting non-newtonian power-law fluid over a non-linearly stretching surface along with porous plate in porous medium. The governing equations are reduced to non-linear ordinary differential equations by means of similarity transformations. These equations are then solved numerically with the help ofRunge – Kutta shooting method. The effect of various flow parameters in the form of dimensionless quantities on the flow field are discussed and presented graphically.

Swimming microorganisms often have to propel in complex, non-Newtonianfluids. We carry out experiments with self-propelling helical swimmers driven by an externally rotating magnetic field in shear-thinning, inelastic fluids. Similarly to swimming in a Newtonian fluid, we obtain for each fluid a locomotion speed which scales linearly with the rotation frequency of the swimmer, but with a prefactor which depends on the power index of the fluid. The fluid is seen to always increase the swimming speed of the helix, up to 50% faster and thus the strongest of such type reported to date. The maximum relative increase for a fluid power index of around 0.6. Using simple scalings, we argue that the speed increase is not due to the local decrease of the flow viscosity around the helical filament but hypothesise instead that it originates from confinement-like effect due to viscosity stratification around the swimmer.

Low-density lipoprotein (LDL), which is recognized as bad cholesterol, typically has been regarded as a main cause of atherosclerosis. LDL infiltration across arterial wall and subsequent formation of Ox-LDL could lead to atherogenesis. In the present study, combined effects of non-Newtonianfluid behavior and fluid-structure interaction (FSI) on LDL mass transfer inside an artery and through its multilayer arterial wall are examined numerically. Navier-Stokes equations for the blood flow inside the lumen and modified Darcy's model for the power-law fluid through the porous arterial wall are coupled with the equations of mass transfer to describe LDL distributions in various segments of the artery. In addition, the arterial wall is considered as a heterogeneous permeable elastic medium. Thus, elastodynamics equation is invoked to examine effects of different wall elasticity on LDL distribution in the artery. Findings suggest that non-Newtonian behavior of filtrated plasma within the wall enhances LDL accumulation meaningfully. Moreover, results demonstrate that at high blood pressure and due to the wall elasticity, endothelium pores expand, which cause significant variations on endothelium physiological properties in a way that lead to higher LDL accumulation. Additionally, results describe that under hypertension, by increasing angular strain, endothelial junctions especially at leaky sites expand more dramatic for the high elastic model, which in turn causes higher LDL accumulation across the intima layer and elevates atherogenesis risk.

We solve the stationary Stokes and Navier-Stokes equations for non-Newtonian incompressible fluids with shear dependent viscosity in domains with outlets containing unbounded cross sections, in the case of shear thickening viscosity. The flux assumes arbitrary given values and the growth of the cross sections are analyzed under different convergence hypotheses, inclusive the growth of Dirichlet's integral of the velocity field is deeply related the convergence hypotheses of such sections. We extend the results of the section 4 of [12, Ladyzhenskaya and Solonnikov] (for Newtonian fluids) to non-Newtonianfluids using the techniques found in [3, Dias and Santos].

In this work, non-Newtonian effects on Low-Density Lipoprotein (LDL) transport across an artery are analyzed with a multi-layer model. Four rheological models (Carreau, Carreau-Yasuda, power-law and Newtonian) are used for the blood flow through the lumen. For the non-Newtonian cases, the arterial wall is modeled with a generalized momentum equation. Convection-diffusion equation is used for the LDL transport through the lumen, while Staverman-Kedem-Katchalsky, combined with porous media equations, are used for the LDL transport through the wall. Results are presented in terms of filtration velocity, Wall Shear Stresses (WSS) and concentration profiles. It is shown that non-Newtonian effects on mass transport are negligible for a healthy intramural pressure value. Non-Newtonian effects increase slightly with intramural pressure, but Newtonian assumption can still be considered reliable. Effects of arterial size are also analyzed, showing that Newtonian assumption can be considered valid for both medium and large arteries, in predicting LDL deposition. Finally, non-Newtonian effects are also analyzed for an aorta-common iliac bifurcation, showing that Newtonian assumption is valid for mass transport at low Reynolds numbers. At a high Reynolds number, it has been shown that a non-Newtonianfluid model can have more impact due to the presence of flow recirculation.

water can remarkably reduce the frictional resistance to flow. The material sodium carboxymethylcellulose was added to fresh water and subjected to...pipe friction tests under a wide range of shear rates, additive concentration, and temperature conditions. The frictional data are characterized by application of the power law expression for non-Newtonianfluids. (Author)

A numerical analysis of Newtonian and non-Newtonian flow in an axi-symmetric tube with a local constriction simulating a stenosed artery under steady and pulsatile flow conditions was carried out. Based on these results, the concentration fields of LDL ( low density lipoprotein ) and Albumin were discussed. According to the results, in great details the macromolecule transport influences of wall shear stress, non-Newtonianfluid character and the scale of the molecule etc are given. The results of Newtonian fluid flow and nonNewtonianfluid flow , steady flow and pulsatile flow are compared. These investigations can provide much valuable information about the correlation between the flow properties, the macromolecule transport and the development of atherosclerosis.

Full Text Available The problem of the effect of Joule heating generation on the hydrodynamic profile and the solute transport found in electrophoretic devices is addressed in this article. The research is focused on the following two problems: The first one is centered around the effect of Joule heating on the hydrodynamic velocity profile and it is referred to as "the carrier fluid problem." The other one is related to the effect of Joule heating on the solute transport inside electrophoretic cells and it is referred to as "the solute problem". The hydrodynamic aspects were studied first to yield the velocity profiles required for analysis of the solute transport problem. The velocity profile obtained in this study is analytical and the results are valid for non-Newtonianfluids carriers. To this end, the power-law model was used to study the effect of the rheology of the material in conjunction with the effect of Joule heating generation inside batch electrophoretic devices. This aspect of the research was then effectively used to study the effect of Joule heating generation on the motion of solutes (such as macromolecules under the influence of non-Newtonian carriers. This aspect of the study was performed using an area-averaging approach that yielded analytical results for the effective diffusivity of the device.

The local overall volumetric gas-liquid mass transfer coefficients at the specified point in a gas-liquid-solid three-phase reversed flow jet loop bioreactor (JLB) with a non-Newtonianfluid was experimentally investigated by a transient gassing-in method. The effects of liquid jet flow rate, gas jet flow rate, particle density, particle diameter, solids loading, nozzle diameter and CMC concentration on the local overall volumetric gas-liquid mass transfer coefficient (K(L)a) profiles were discussed. It was observed that local overall K(L)a profiles in the three-phase reversed flow JLB with non-Newtonianfluid increased with the increase of gas jet flow rate, liquid jet flow rate, particle density and particle diameter, but decreased with the increase of the nozzle diameter and CMC concentration. The presence of solids at a low concentration increased the local overall K(L)a profiles, and the optimum of solids loading for a maximum profile of the local overall K(L)a was found to be 0.18x10(-3)m(3) corresponding to a solids volume fraction, varepsilon(S)=2.8%.

Full Text Available The Shear Thickening Fluid (STF is a dilatant material, which displays non-Newtonian characteristics in its unique ability to transit from a low viscosity fluid to a high viscosity fluid. The research performed investigates the STF behavior by modeling and simulation of the interaction between the base flow and embedded rigid particles when subjected to shear stress. The model considered the Lagrangian description of the rigid particles and the Eulerian description of fluid flow. The numerical analysis investigated key parameters such as applied flow acceleration, particle distribution and arrangement, volume concentration of particles, particle size, shape and their behavior in a Newtonian and non-Newtonianfluid base. The fluid-particle interaction model showed that the arrangement, size, shape and volume concentration of the particles had a significant effect on the behavior of the STF. Although non-conclusive, the addition of particles in non-Newtonianfluids showed a promising trend of improved shear thickening effects at high shear strain rates.

运用计算流体动力学(CFD)方法分别对旋流器内非牛顿流体与牛顿流体的流场分别进行数值模拟.分析采用RSM(SSG)雷诺应力模型,得到非牛顿流体与牛顿流体的速度场、压力场以及表观粘度分布规律.研究结果揭示了非牛顿流体在分离旋流器内的流场特性:由于受非牛顿流体表现粘度随剪切速率变化的影响,在同一位置处,非牛顿流体的静压力、轴向速度以及径向速度都大于牛顿流体,而切向速度小于牛顿流体；同时,旋流器内非牛顿流体的零轴速包络面(LZVV)比牛顿流体更加靠近器壁,这导致旋流器中非牛顿流体在同等条件下比牛顿流体的分离效率低；以上这些特性为进一步充分认识用于分离非牛顿流体的旋流器分离机理提供依据.%The method of Computational Fluid Dynamics was used to simulate the fluid field of the non-Newtonianfluid and the Newtonian fluid in the hydrocyclone. The Analysis was operated by reynolds stress model and obtained the velocity field,the pressure field as well as the apparent viscosity distribution of non-Newtonianfluid and the Newtonian fluid. The results revealed the Flow field Characteristics of the non-Newtonianfluids in the hydrocyclone: In the same position .with the effect of apparent viscosity changes of non-Newtonianfluid,the static pressure,the axial velocity as well as radial velocity of non-Newtonianfluid were bigger than Newtonian fluid's.and the radial velocity was less; The locus of zero vertical velocity of hydrocyclone of non-Newtonian was closer to the wall;these characteristics led to lower separation efficiency of non-Newtonianfluid than Newtonian fluid's under the same conditions. This study provided the evidence for new understand of the separation mechanism of non-Newtonianfluid.

Polymeric enrobing flows are important in industrial manufacturing technology and process systems. Such flows are non-Newtonian. Motivated by such applications, in this article we investigate the nonlinear steady state boundary layer flow, heat, and mass transfer of an incompressible Jefferys non-Newtonianfluid past a vertical porous plate in a non-Darcy porous medium. The transformed conservation equations are solved numerically subject to physically appropriate boundary conditions using a versatile, implicit, Keller-box finite-difference technique. The numerical code is validated with previous studies. The influence of a number of emerging non-dimensional parameters, namely Deborah number (De), Darcy number (Da), Prandtl number (Pr), ratio of relaxation to retardation times (λ), Schmidt number (Sc), Forchheimer parameter (Λ), and dimensionless tangential coordinate (ξ) on velocity, temperature, and concentration evolution in the boundary layer regime are examined in detail. Furthermore, the effects of these parameters on surface heat transfer rate, mass transfer rate, and local skin friction are also investigated. It is found that the boundary layer flow is decelerated with increasing De and Forchheimer parameter, whereas temperature and concentration are elevated. Increasing λ and Da enhances the velocity but reduces the temperature and concentration. The heat transfer rate and mass transfer rates are found to be depressed with increasing De and enhanced with increasing λ. Local skin friction is found to be decreased with a rise in De, whereas it is elevated with increasing λ. An increasing Sc decreases the velocity and concentration but increases temperature.

实验测定了低气速下CO2气泡群在牛顿流体、剪切变稀流体及黏弹性流体中的气含率.讨论了流体的流变性、质量分数及表观气速对气含率的影响.结果表明:在3种不同性质的流体中,气含率均随表观气速的增大而增大.同时发现流体性质对气含率具有不同的影响:对于牛顿流体,表观气速较低时,质量分数对气含率影响可忽略；对于非牛顿流体,气含率随着流动指数n的减小而减小,即剪切变稀效应对气含率有负作用,而黏弹性对气含率的影响可忽略.气含率是气液传质过程设计中最重要的参数,因此研究结果为进一步研究CO2气泡群在非牛顿流体中的传质奠定了一定基础.%The gas holdups of CO2 bubble swarm at low superficial gas velocity in Newtonian fluid, shear thinned fluid and viscoelastic fl uid were measured. The influences of rheological property, mass fraction and superficial gas velocity on the gas holdup were investigated. The results show that the gas holdups in three fluids all increase with the increase of superficial gas velocity, and different fluid has different effects on the gas holdup. The effect of mass fraction on the gas holdup in Newtonian fluid at low superficial gas velocity is negligible. For non-Newtonianfluid, the gas holdup decreases with the decrease of flow index n, that is, shear thinning effect has negative impact on the gas holdup, and the influence of viscoelasticity on the gas holdup is negligible. The gas holdup is the most important parameter for the gas-liquid mass transfer process design, and it provides a solid foundation for the research on mass transfer of CO2 bubble swarm in non-Newtonianfluid.

A numerical analysis of non-Newtonianfluid flow in non-planar artery with bifurcation was performed by using a finite element method to solve the three-dimensional Navier-Stokes equations coupled with the non-Newtonian constitutive models, including Carreau,Cross and Bingham models. The objective of this study is to investigate the effects of the non-Newtonian properties of blood as well as curvature and out-of-plane geometry in the non-planar daughter vessels on the velocity distribution and wall shear stress. The results of this study support the view that the non-planarity of blood vessels and the non-Newtonian properties of blood are of important in hemodynamics and play a significant role in vascular biology and pathophysiology.

Full Text Available Mean and rms velocity characteristics of two Newtonian flows at Reynolds numbers of 12,800 (glycerin solution and 48,000 (water and of a non-Newtonian flow (0.2% CMC solution, at a power number similar to the Newtonian glycerin flow in a mixing vessel stirred by a 60° pitched blade impeller have been measured by laser Doppler velocimetry (LDV. The velocity measurements, resolved over 360° and 1.08° of impeller rotation, showed that the mean flow of the two power number matched glycerin and CMC flows were similar to within 3% of the impeller tip velocity and the turbulence intensities generally lower in the CMC flow by up to 5% of the tip velocity. The calculated mean flow quantities showed similar discharge coefficient and pumping efficiency in all three flows and similar strain rate between the two power number matched glycerin and CMC flows; the strain rate of the higher Reynolds number Newtonian flow was found to be slightly higher. The energy balance around the impeller indicated that the CMC flow dissipated up to 9% more of the total input power and converted 7% less into the turbulence compared to the glycerin flow with the same power input which could lead to less effective mixing processes where the micro-mixing is important.

Steady flow and physiological pulsatile flow in a rigid 180° curved tube are investigated using particle image velocimetry. A non-Newtonian blood-analog fluid is used, and in-plane primary and secondary velocity fields are measured. A vortex detection scheme ( d 2-method) is applied to distinguish vortical structures. In the pulsatile flow case, four different vortex types are observed in secondary flow: deformed-Dean, Dean, Wall and Lyne vortices. Investigation of secondary flow in multiple cross sections suggests the existence of vortex tubes. These structures split and merge over time during the deceleration phase and in space as flow progresses along the 180° curved tube. The primary velocity data for steady flow conditions reveal additional vortices rotating in a direction opposite to Dean vortices—similar to structures observed in pulsatile flow—if the Dean number is sufficiently high.

The problem of a magneto-hydro dynamic flow and heat transfer to a non-Newtonian power-law fluid flow past a continuously moving flat porous plate in the presence of sucion/injection with heat flux by taking into consideration the viscous dissipation is analysed. The non-linear partial differential equations governing the flow and heat transfer are transformed into non-linear ordinary differential equations using appropriate transformations and then solved numerically by an implicit finite difference scheme. The solution is found to be dependent on various governing parameters including the magnetic field parameter M, power-law index n, suction/injection parameter ƒw, Prandtl number Pr and Eckert number Ec. A systematical study is carried out to illustrate the effects of these major parameters on the velocity profiles, temperature profile, skin friction coefficient and rate of heat transfer and the local Nusslet number.

Full Text Available The laminar boundary layer flow and heat transfer of Casson non-Newtonianfluid from an inclined (solar collector plate in the presence of thermal and hydrodynamic slip conditions is analysed. The inclined plate surface is maintained at a constant temperature. The boundary layer conservation equations, which are parabolic in nature, are normalized into non-similar form and then solved numerically with the well-tested, efficient, implicit, stable Keller-box finite-difference scheme. Increasing velocity slip induces acceleration in the flow near the inclined plate surface. Increasing velocity slip consistently enhances temperatures throughout the boundary layer regime. An increase in thermal slip parameter strongly decelerates the flow and also reduces temperatures in the boundary layer regime. An increase in Casson rheological parameter acts to elevate considerably the velocity and this effect is pronounced at higher values of tangential coordinate. Temperatures are however very slightly decreased with increasing values of Casson rheological parameter.

Full Text Available The effects of MHD free convection heat and mass transfer of power-law Non-Newtonianfluids along a stretching sheet with viscous dissipation has been analyzed. This has been done under the simultaneous action of suction, thermal radiation and uniform transverse magnetic field. The stretching sheet is assumed to continuously moving with a power-law velocity and maintaining a uniform surface heat-flux. The governing non-linear partial differential equations are transformed into non-linear ordinary differential equations, using appropriate similarity transformations and the resulting problem is solved numerically using Nachtsheim-Swigert shooting iteration technique along with sixth order Runge-Kutta integration scheme. A parametric study of the parameters arising in the problem such as the Eckert number due to viscous dissipation, radiation number, buoyancy parameter, Schmidt number, Prandtl number etc are studied and the obtained results are shown graphically and the physical aspects of the problem are discussed.

This paper is concerned with the forced convective heat transfer of dilute liquid suspensions of nanoparticles (nanofluids) flowing through a straight pipe under laminar conditions. Stable nanofluids are formulated by using the high shear mixing and ultrasonication methods. They are then characterised for their size, surface charge, thermal and rheological properties and tested for their convective heat transfer behaviour. Mathematical model-ling is performed to simulate the convective heat transfer of nanofluids using a single phase flow model and con-sidering nanofluids as both Newtonian and non-Newtonianfluid. Both experiments and mathematical modelling show that nanofluids can substantially enhance the convective heat transfer. Analyses of the results suggest that the non-Newtonian character of nanofluids influences the overall enhancement, especially for nanofluids with an obvious non-Newtonian character.

In this paper, the migration of secondary particles in a non-Newtonian ceramic slurry inthe tape casting process is investigated with the purpose of understanding the particle distribution patterns along the casting direction. The Ostwald-de Waele power law model for the non-Newtonian flow...

The authors consider a non-Newtonianfluid governed by equations with p-structure in a cubic domain.A fluid is said to be shear thinning (or pseudo-plastic) if 1 ＜p ＜ 2,and shear thickening (or dilatant) if p ＞ 2.The case p ＞ 2 is considered in this paper.To improve the regularity results obtained by Crispo,it is shown that the second-order derivatives of the velocity and the first-order derivative of the pressure belong to suitable spaces,by appealing to anisotropic Sobolev embeddings.

The mechanics of air sparger systems have been primarily investigated for aqueous-based Newtonian fluids. Tilton et al. (1982) [1] describes the fluid mechanics of air sparging systems in non-Newtonianfluids as having two primary flow regions. A center region surrounding the sparger, referred to as the region of bubbles (ROB), contains upward flow due to the buoyant driving force of the rising bubbles. In an annular region, outside the ROB, referred to as the zone of influence (ZOI), the fluid flow is reversed and is opposed to the direction of bubble rise. Outside the ZOI the fluid is unaffected by the air sparger system. The flow regime in the ROB is often turbulent, and the flow regime in the ZOI is laminar; the flow regime outside the ZOI is quiescent. Tests conducted with shear thinning non-Newtonianfluid in a 34-in. diameter tank showed that the ROB forms an approximately inverted cone that is the envelop of the bubble trajectories. The depth to which the air bubbles reach below the sparger nozzle is a linear function of the air-flow rate. The recirculation time through the ZOI was found to vary proportionally with the inverse square of the sparging air-flow rate. Visual observations of the ROB were made in both water and Carbopol®. The bubbles released from the sparge tube in Carbopol® were larger than those in water

Full Text Available Blood is in fact a suspension of different cells with yield stress, shear thinning, and viscoelastic properties, which can be represented by different non-Newtonian models. Taking Casson fluid as an example, an unsteady solver on unstructured grid for non-Newtonianfluid is developed to simulate transient blood flow in complex flow region. In this paper, a steady solver for Newtonian fluid is firstly developed with the discretization of convective flux, diffusion flux, and source term on unstructured grid. For the non-Newtonian characteristics of blood, the Casson fluid is approximated by the Papanastasiou's model and treated as Newtonian fluid with variable viscosity. Then considering the transient property of blood flow, an unsteady non-Newtonian solver based on unstructured grid is developed by introducing the temporal term by first-order upwind difference scheme. Using the proposed solver, the blood flows in carotid bifurcation of hypertensive patients and healthy people are simulated. The result shows that the possibility of the genesis and development of atherosclerosis is increased, because of the increase in incoming flow shock and backflow areas of the hypertensive patients, whose WSS was 20~87.1% lower in outer vascular wall near the bifurcation than that of the normal persons and 3.7~5.5% lower in inner vascular wall downstream the bifurcation.

The rimming flow of a viscoelastic thin film inside a rotating horizontal cylinder is studied theoretically. Attention is given to the onset of non-Newtonian free-surface instability in creeping flow. This non-inertial instability has been observed in experiments, but current theoretical models of Newtonian fluids can neither describe its origin nor explain its onset. This study examines two models of nonNewtonianfluids to see if the experimentally observed instability can be predicted analytically. The non-Newtonian viscosity and elastic properties of the fluid are described by the Generalized Newtonian Fluid (GNF) and Second Order Viscoelastic Fluid (SOVF) constitutive models, respectively. With linear stability analysis, it is found that, analogously to the Newtonian fluid, rimming flow of viscous non-Newtonianfluids (modeled by GNF) is neutrally stable. However, the viscoelastic properties of the fluid (modeled by SOVF) are found to contribute to the flow destabilization. The instability is shown to in...

The annular solidification of an aluminium-silicon alloy in a graphite mould with a geometry consisting of horizontal concentric cylinders is studied numerically. The analysis incorporates the behavior of non-Newtonian, pseudoplastic (n=0.2), Newtonian (n=1), and dilatant (n=1.5) fluids. The fluid mechanics and heat transfer coupled with a transient model of convection diffusion are solved using the finite volume method and the SIMPLE algorithm. Solidification is described in terms of a liquid fraction of a phase change that varies linearly with temperature. The final results make it possible to infer that the fluid dynamics and heat transfer of solidification in an annular geometry are affected by the non-Newtonian nature of the fluid, speeding up the process when the fluid is pseudoplastic. (orig.)

Full Text Available Abstract In this work, a simplified kick simulator is developed using the ANSYS® CFX software in order to better understand the phenomena called kick. This simulator is based on the modeling of a petroleum well where a gas kick occurs. Dynamic behavior of some variables like pressure, viscosity, density and volume fraction of the fluid is analyzed in the final stretch of the modeled well. In the simulations nine different drilling fluids are used of two rheological categories, Ostwald de Waele, also known as Power-Law, and Bingham fluids, and the results are compared among them. In these comparisons what fluid allows faster or slower invasion of gas is analyzed, as well as how the gas spreads into the drilling fluid. The pressure behavior during the kick process is also compared t. It is observed that, for both fluids, the pressure behavior is similar to a conventional leak in a pipe.

Full Text Available An analytic solution of the flow of a third-grade fluid on a porous plate is constructed. The porous plate is executing oscillations in its own plane with superimposed injection or suction. An increasing or decreasing velocity amplitude of the oscillating porous plate is also examined. It is also shown that in case of third-grade fluid, a combination of suction/injection and decreasing/increasing velocity amplitude is possible as well. Several limiting situations with their implications are given and discussed.

Full Text Available The identification of non-ideal flows in a continuous-flow mixing of non-Newtonianfluids is a challenging task for various chemical industries: plastic manufacturing, water and wastewater treatment, and pulp and paper manufacturing. Non-ideal flows such as channelling, recirculation, and dead zones significantly affect the performance of continuous-flow mixing systems. Therefore, the main objective of this paper was to develop an identification protocol to measure non-ideal flows in the continuous-flow mixing system. The extent of non-ideal flows was quantified using a dynamic model that incorporated channelling, recirculation, and dead volume in the mixing vessel. To estimate the dynamic model parameters, the system was excited using a frequency-modulated random binary input by injecting the saline solution (as a tracer into the fresh feed stream prior to being pumped into the mixing vessel. The injection of the tracer was controlled by a computer-controlled on-off solenoid valve. Using the trace technique, the extent of channelling and the effective mixed volume were successfully determined and used as mixing quality criteria. Such identification procedures can be applied at various areas of chemical engineering in order to improve the mixing quality.

Full Text Available A numerical investigation is carried out on an unsteady MHD free convection flow of a well-known non-Newtonian visco elastic second order Rivlin-Erickson fluid past an impulsively started semi-infinite vertical plate in the presence of homogeneous chemical reaction, thermal radiation, thermal diffusion, radiation absorption and heat absorption with constant mass flux. The presence of viscous dissipation is also considered at the plate under the influence of uniform transverse magnetic field. The flow is governed by a coupled nonlinear system of partial differential equations which are solved numerically by using finite difference method. The effects of various physical parameters on the flow quantities viz. velocity, temperature, concentration, Skin friction, Nusselt number and Sherwood number are studied numerically. The results are discussed with the help of graphs. We observed that the velocity decreases with an increase in magnetic field parameter, Schmidt number, and Prandtl number while it increases with an increase in Grashof number, modified Grashof number, visco-elastic parameter and Soret number. Temperature increases with an increase in radiation absorption parameter, Eckert number and visco-elastic parameter while it decreases with increasing values of radiation parameter, Prandtl number and heat absorption parameter. Concentration increases with increase in Soret number while it decreases with an increase in Schmidt number and chemical reaction parameter.

Full Text Available The unsteady flow and heat transfer in an incompressible laminar, electrically conducting and non-Newtonianfluid over a non-isothermal stretching sheet with the variation in the viscosity and thermal conductivity in a porous medium by the influence of an external transverse magnetic field have been obtained and studied numerically. By using similarity analysis the governing differential equations are transformed into a set of non-linear coupled ordinary differential equations which are solved numerically. Numerical results were presented for velocity and temperature profiles for different parameters of the problem as power law parameter, unsteadiness parameter, radiation parameter, magnetic field parameter, porous medium parameter, temperature buoyancy parameter, Prandtl parameter, modified Eckert parameter, Joule heating parameter , heat source/sink parameter and others. A comparison with previously published work has been carried out and the results are found to be in good agreement. Also the effects of the pertinent parameters on the skin friction and the rate of heat transfer are obtained and discussed numerically and illustrated graphically.

The identification of non-ideal flows in a continuous-flow mixing of non-Newtonianfluids is a challenging task for various chemical industries: plastic manufacturing, water and wastewater treatment, and pulp and paper manufacturing. Non-ideal flows such as channelling, recirculation, and dead zones significantly affect the performance of continuous-flow mixing systems. Therefore, the main objective of this paper was to develop an identification protocol to measure non-ideal flows in the continuous-flow mixing system. The extent of non-ideal flows was quantified using a dynamic model that incorporated channelling, recirculation, and dead volume in the mixing vessel. To estimate the dynamic model parameters, the system was excited using a frequency-modulated random binary input by injecting the saline solution (as a tracer) into the fresh feed stream prior to being pumped into the mixing vessel. The injection of the tracer was controlled by a computer-controlled on-off solenoid valve. Using the trace technique, the extent of channelling and the effective mixed volume were successfully determined and used as mixing quality criteria. Such identification procedures can be applied at various areas of chemical engineering in order to improve the mixing quality.

Analysis is carried out to study the existence, uniqueness and behavior of exact solutions of the fourth order nonlinear coupled ordinary differential equations arising in the flow and heat transfer of a viscoelastic, electrically conducting fluid past a continuously stretching sheet. The ranges of the parametric values are obtained for which the system has a unique pair of solutions,a double pair of solutions and infinitely many solutions.

@@ Blood flow under various conditions of vessel is simulated as a non-Newtonianfluid by the two-dimensional Lattice Boltzmann method,in which the Casson model is used to express the relationship between viscosity and shear rate of the blood.The flow field distributions at certain sites near the narrowing and bifurcation of the vessel explain the hemodynamic mechanism of the preclilection of the atherosclerotic lesions for these sites which are consistent with that found by medical studies.

In this study, we investigated inelastic non-Newtonianfluid flow over heterogeneously slippery surfaces. First, we simulated the flow of aqueous xanthan gum solutions over a bubble mattress, which is a superhydrophobic surface consisting of transversely positioned no-slip walls and no-shear gas bubbles. The results reveal that for shear-thinning fluids wall slip can be increased significantly, provided that the system is operated in the shear-thinning regime. For a 0.2 wt% xanthan gum solution with a power-law index of n =0.4 , the numerical results indicate that wall slip can be enhanced 3.2 times when compared to a Newtonian liquid. This enhancement factor was also predicted from a theoretical analysis, which gave an expression for the maximum slip length that can be attained over flat, heterogeneously slippery surfaces. Although this equation was derived for a no-slip/no-shear unit length that is much larger than the typical size of the system, we found that it can also be used to predict the enhancement in the regime where the slip length is proportional to the size of the no-shear region or the bubble width. The results could be coupled to the hydrodynamic development or entrance length of the system, as maximum wall slip is only reached when the fluid flow can fully adapt to the no-slip and no-shear conditions at the wall.

Full Text Available This study is based upon constructing a new class of closed-form shock wave solutions for some nonlinear problems arising in the study of a third grade fluid model. The Lie symmetry reduction technique has been employed to reduce the governing nonlinear partial differential equations into nonlinear ordinary differential equations. The reduced equations are then solved analytically, and the shock wave solutions are constructed. The conditions on the physical parameters of the flow problems also fall out naturally in the process of the derivation of the solutions.

Mixed convection flow of electrically conducting power law fluids along a vertical wavy surface in the presence of a transverse magnetic field is studied numerically. Prandtl coordinate transformation together with the spline alternating direction implicit method is employed to solve the boundary layer equations. The influences of both flow structure and dominant convection mode on the overall parameters of flow and heat transfer are well discussed. Also, the role of magnetic field in controlling the boundary layers is investigated. The variation of Nusselt number and skin friction coefficient are studied as functions of wavy geometry, magnetic field, buoyancy force and material parameters. Results reveal the interrelation of the contributing factors.

We investigate the externally time-dependent pulsatile electrokinetic viscous flows by extending the previous simulations concerning the electrokinetic microfluidics for different geometries. The external body force originated from between the nonlinear Poisson-Boltzmann field and the flow-induced electric field is employed in the Cauchy momentum equation, and then the Nernst-Planck equation in connection with the net current conservation is coupled. Our explicit model allows one to quantify the effects of the oscillating frequency and conductance of the Stern layer, considering the shear thinning effect and the strong electric double layer interaction. This presentation reports the new results regarding the implication of optimum frequency pressure pulsations toward realizing mechanical to electrical energy transfer with high conversion efficiencies. These combined factors for different channel dimension are examined in depth to obtain possible enhancements of streaming current, with taking advantage of pulsating pressure field. From experimental verifications by using electrokinetic power chip, it is concluded that our theoretical framework can serve as a useful basis for micro/nanofluidics design and potential applications to the enhanced energy conversion. NRF of Korea (No.2015R1A2A1A15052979) and KIST (No.2E26490).

This is a discussion of non-invasive determination of the viscosity of a non-Newtonianfluid in laminar pipe flow over the range of shear rates present in the pipe. The procedure requires knowledge of the flow profile in and the pressure drop along the long straight run of pipe. The profile is determined by using a pulsed ultrasonic Doppler velocimeter. This approach is ideal for making non-invasive, real-time measurements for monitoring and control. Rheograms of a shear thinning, thixotropic gel which is often used as a Hanford waste simulant are presented. The operating parameters and limitations of the ultrasound based instrument will be discussed. The component parts of the instrument have been packaged into a unit for field use. The presentation also discusses the features and engineering optimizations done to enhance field usability of the instrument.

: The effective dynamic viscosity was measured in the graphite water-based nanofluids. The shear thinning non-Newtonian behavior is observed in the measurement. On the basis of the best fitting of the experimental data, the viscosity at zero shear rate or at infinite shear rate is determined for each of the fluids. It is found that increases of the particle volume concentration and the holding time period of the nanofluids result in an enhancement of the effective dynamic viscosity. The maximum enhancement of the effective dynamic viscosity at infinite rate of shear is more than 24 times in the nanofluids held for 3 days with the volume concentration of 4% in comparison with the base fluid. A transmission electron microscope is applied to reveal the morphology of aggregated nanoparticles qualitatively. The large and irregular aggregation of the particles is found in the 3-day fluids in the drying samples. The Raman spectra are extended to characterize the D and G peaks of the graphite structure in the nanofluids. The increasing intensity of the D peak indicates the nanoparticle aggregation growing with the higher concentration and the longer holding time of the nanofluids. The experimental results suggest that the increase on effective dynamic viscosity of nanofluids is related to the graphite nanoparticle aggregation in the fluids.

Full Text Available The paper presents a numerical investigation of non-Newtonian modeling effects on unsteady periodic flows in a two-dimensional (2D pipe with two idealized stenoses of 75% and 50% degrees, respectively. The governing Navier-Stokes equations have been modified using the Cartesian curvilinear coordinates to handle complex geometries. The investigation has been carried out to characterize four different non-Newtonian constitutive equations of blood, namely, the (i Carreau, (ii Cross, (iii Modified Casson, and (iv Quemada models. The Newtonian model has also been analyzed to study the physics of fluid and the results are compared with the non-Newtonian viscosity models. The numerical results are represented in terms of streamwise velocity, pressure distribution, and wall shear stress (WSS as well as the vorticity, streamlines, and vector plots indicating recirculation zones at the poststenotic region. The results of this study demonstrate a lower risk of thrombogenesis at the downstream of stenoses and inadequate blood supply to different organs of human body in the Newtonian model compared to the non-Newtonian ones.

Collision of Newtonian liquid droplets has been extensively investigated both experimentally and numerically for decades. Limited information, however, is available about non-Newtonian droplet collision dynamics. In the present work, high-fidelity numerical simulations were performed to study the situation associated with shear-thinning non-Newtonian liquids. The formulation is based on a complete set of conservation equations for the liquid and the surrounding gas phases. An improved volume-of-fluid (VOF) method, combined with an innovative topology-oriented adaptive mesh refinement (TOAMR) technique, was developed and implemented to track the interfacial dynamics. The complex evolution of the droplet surface over a broad range of length scales was treated accurately and efficiently. In particular, the thin gas film between two approaching droplets and subsequent breakup of liquid threads were well-resolved. Various types of droplet collision were obtained, including coalescence, bouncing, and reflexive and stretching separations. A regime diagram was developed and compared with that for Newtonian liquids. Fundamental mechanisms and key parameters that dictate droplet behaviors were identified. In addition, collision-induced atomization was addressed. This work was sponsored by the U.S. Army Research Office under the Multi-University Research Initiative under contract No. W911NF-08-1-0124. The support and encouragement provided by Dr. Ralph Anthenien are gratefully acknowledged.

The onset of transient convection in non-Newtonian liquid immersing porous media was simulated using a Computational Fluid Dynamics (CFD) package for the thermal boundary condition of Fixed Surface Temperature (FST). Most of the simulated values of stability criteria were found to be in good agreement with the predicted and theoretical values of transient critical Rayleigh number for non-Newtonian liquid defined by Tan and Thorpe (1992) for power-law fluids. The critical transient Rayleigh numbers for convection in porous media were found to be in good agreement with theoretical values by using apparent viscosity µapp at zero shear. The critical time and critical depth for transient heat conduction were then determined accurately that

The spiral component of blood flow has both beneficial and detrimental effects in human circulatory system. A numerical investigation is carried out to analyze the effect of spiral blood flow through an axisymmetric three dimensional artery having 75% stenosis at the center. Blood is assumed as a Non-Newtonianfluid. Standard k-ω model is used for the simulation with the Reynolds number of 1000. A parabolic velocity profile with spiral flow is used as inlet boundary condition. The peak values of all velocity components are found just after stenosis. But total pressure gradually decreases at downstream. Spiral flow of blood has significant effects on tangential component of velocity. However, the effect is mild for radial and axial velocity components. The peak value of wall shear stress is at the stenosis zone and decreases rapidly in downstream. The effect of spiral flow is significant for turbulent kinetic energy. Detailed investigation and relevant pathological issues are delineated throughout the paper.

Many of the biological fluids analyzed in Lab-on-a-Chip systems contain elastic components, which gives the fluids elastic character. Such fluids are said to be non-Newtonian or, more precisely, viscoelastic. They can give rise to exotic effects on the macroscale, which are never seen for fluids...... with components relying on viscoelastic effects, but the non-intuitive nature of these fluids complicates the design process. This thesis combines the method of topology optimization with differential constitutive equations, which govern the flow of viscoelastic fluids. The optimization method iteratively...... experimentally, and compared the results with the established hyperbolic designs. We found superior performance in the parameter regime of the optimization as well as similar optimal performance [P3]. The cross-slot geometry is known to exhibit bistability for viscoelastic fluids. We studied this geometry...

A theory is presented to describe the apparent viscosity of thixotropic fluids as a function of the rate of shear. It represents the extension of a semiclassical approach that was previously formulated to deal with matter densification phenomena in solids starting from the state equation of the medium. In this context, the Debye expression for the Helmholtz free energy has been provided with a density of vibrational modes that accounts for atomic and microstructural changes occurring at the frequency scale of momentum transport (see diffusion). Working out the steady-state condition with respect to time gives an equation relating reduced apparent viscosity (η˜) and shear rate (γ˜) through the temperature value (θ*) that is energetically equivalent to the medium vibrations implied. Viscosity also turns out to depend on the Debye temperature θD (see φ˜θ*/θD) and an equivalent Gruneisen parameter (μ), defined with respect to viscosity variations. Increasing φ in pseudoplastic and dilatant media, respectively, increases and decreases η˜, which always increases with increasing μ. The analogy between dilatancy/sintering and pseudoplasticity/desintering is suggested, and a correspondence between matter and momentum transports is traced on the basis of the phononic spectrum properties. Application to experimental measurements are presented and discussed for aqueous monodispersions of polystyrene (PS) latex particles, aqueous glycerol solutions of partially hydrolyzed polyacrylamide (PHPAA) at different sodium chloride (NaCl) concentrations, polymethylmethacrylate (PMMA) suspensions in dioctylphthalate (DOP), and for a molecularly thin liquid film of octamethylciclotetrasiloxane (OMCTS). Best fit coefficients for φ and μ have been constrained to the Debye temperature and the effective low-shear viscosity (η0) according to their dependences upon the suspended volume fraction (φ), θD=θD(φ), and η0=η0(φ), and the agreement with experimental data is

A miniaturised fibre optic laser-Doppler anemometer was used to carry out a detailed hydrodynamic investigation of the flow downstream of a sudden expansion with 0.1-0.2% by weight shear-thinning aqueous solutions of xanthan gum. Upstream of the sudden expansion the pipe flow was fully-developed and the xanthan gum solutions exhibited drag reduction with corresponding lower radial and tangential normal Reynolds stresses, but higher axial Reynolds stress near the wall and a flatter axial mean velocity profile in comparison with Newtonian flow. The recirculation bubble length was reduced by more than 20% relative to the high Reynolds number Newtonian flow, and this was attributed to the occurrence further upstream of high turbulence for the non-Newtonian solutions, because of advection of turbulence and earlier high turbulence production in the shear layer. Comparisons with the measurements of Escudier and Smith (1999) with similar fluids emphasized the dominating role of inlet turbulence. The present was less anisotropic, and had lower maximum axial Reynolds stresses (by 16%) but higher radial turbulence (20%) than theirs. They reported considerably longer recirculating bubble lengths than we do for similar non-Newtonianfluids and Reynolds numbers. (orig.)

Full Text Available In view of the limitations of the existing Newton fluid effects on the vortex flow mechanism study, numerical analysis of non Newton fluid effects was presented. Using Reynolds stress turbulence model (RSM and mixed multiphase flow model (Mixture of FLUENT (fluid calculation software and combined with the constitutive equation of apparent viscosity of non-Newtonianfluid, the typical non-Newtonianfluid (drilling fluid, polymer flooding sewage and crude oil as medium and Newton flow field (water as medium were compared by quantitative analysis. Based on the research results of water, the effects of non-Newtonian rheology on the key parameters including the combined vortex motion index n and tangential velocity were analyzed. The study shows that: non-Newtonian rheology has a great effect on tangential velocity and n value, and tangential velocity decreases with non-Newtonian increasing. The three kinds of n values (constant segment are: 0.564(water, 0.769(polymer flooding sewage, 0.708(drilling fluid and their variation amplitudes are larger than Newtonian fluid. The same time, non-Newtonian rheology will lead to the phenomenon of turbulent drag reduction in the vortex flow field. Compared with the existing formula calculation results shown, the calculation result of non-Newtonian rheology is most consistent with the simulation result, and the original theory has large deviations. The study provides reference for theory research of non-Newtonian cyclone separation flow field.

Flow of non-Newtonianfluids through porous media at high Reynolds numbers is often encountered in chemical, pharmaceutical and food as well as petroleum and groundwater engineering and in many other industrial applications (1 - 2). In particular, the use of shear thinning polymeric solutions has been recently proposed to improve colloidal stability of micro- and nanoscale zerovalent iron particles (MZVI and NZVI) for groundwater remediation. In all abovementioned applications, it is of paramount importance to correctly predict the pressure drop resulting from non-Newtonianfluid flow through the porous medium. For small Reynolds numbers, usually up to 1, typical of laboratory column tests, the extended Darcy law is known to be applicable also to nonNewtonianfluids, provided that all non-Newtonian effects are lumped together into a proper viscosity parameter (1,3). For higher Reynolds numbers (eg. close to the injection wells) non linearities between pressure drop and flow rate arise, and the Darcy-Forchheimer law holds for Newtonian fluids, while for non-Newtonianfluids, it has been demonstrated that, at least for simple rheological models (eg. power law fluids) a generalized Forchheimer law can be applied, even if the determination of the flow parameters (permeability K, inertial coefficient β, and equivalent viscosity) is not straightforward. This work (co-funded by European Union project AQUAREHAB FP7 - Grant Agreement Nr. 226565) aims at proposing an extended formulation of the Darcy-Forchheimer law also for shear-thinning fluids, and validating it against results of pore-scale simulations via computational fluid dynamics (4). Flow simulations were performed using Fluent 12.0 on four different 2D porous domains for Newtonian and non-Newtonianfluids (Cross, Ellis and Carreau models). The micro-scale flow simulation results are analyzed in terms of 'macroscale' pressure drop between inlet and outlet of the model domain as a function of flow rate. The

The self-diffusion coefficients of nematic phases of various model systems consisting of regular convex calamitic and discotic ellipsoids and non-convex bodies such as bent-core molecules and soft ellipsoid strings have been obtained as functions of the shear rate in a shear flow. Then the self-diffusion coefficient is a second rank tensor with three different diagonal components and two off-diagonal components. These coefficients were found to be determined by a combination of two mechanisms, which previously have been found to govern the self-diffusion of shearing isotropic liquids, namely, (i) shear alignment enhancing the diffusion in the direction parallel to the streamlines and hindering the diffusion in the perpendicular directions and (ii) the distortion of the shell structure in the liquid whereby a molecule more readily can escape from a surrounding shell of nearest neighbors, so that the mobility increases in every direction. Thus, the diffusion parallel to the streamlines always increases with the shear rate since these mechanisms cooperate in this direction. In the perpendicular directions, these mechanisms counteract each other so that the behaviour becomes less regular. In the case of the nematic phases of the calamitic and discotic ellipsoids and of the bent core molecules, mechanism (ii) prevails so that the diffusion coefficients increase. However, the diffusion coefficients of the soft ellipsoid strings decrease in the direction of the velocity gradient because the broadsides of these molecules are oriented perpendicularly to this direction due the shear alignment (i). The cross coupling coefficient relating a gradient of tracer particles in the direction of the velocity gradient and their flow in the direction of the streamlines is negative and rather large, whereas the other coupling coefficient relating a gradient in the direction of the streamlines and a flow in the direction of the velocity gradient is very small.

Given the current emphasis on accurate computational fluid dynamics (CFD) modeling of cardiovascular flows, which incorporates realistic blood vessel geometries and cardiac waveforms, it is necessary to revisit the conventional wisdom regarding the influences of non-Newtonian effects. In this study, patient-specific reconstructed 3D geometries, whole blood viscosity data, and venous pulses postdialysis access surgery are used as the basis for the hemodynamic simulations of renal failure patients with native fistula access. Rheological analysis of the viscometry data initially suggested that the correct choice of constitutive relations to capture the non-Newtonian behavior of blood is important because the end-stage renal disease (ESRD) patient cohort under observation experience drastic variations in hematocrit (Hct) levels and whole blood viscosity throughout the hemodialysis treatment. For this purpose, various constitutive relations have been tested and implemented in CFD practice, namely Quemada and Casson. Because of the specific interest in neointimal hyperplasia and the onset of stenosis in this study, particular attention is placed on differences in nonhomeostatic wall shear stress (WSS) as that drives the venous adaptation process that leads to venous geometric evolution over time in ESRD patients. Surprisingly, the CFD results exhibit no major differences in the flow field and general flow characteristics of a non-Newtonian simulation and a corresponding identical Newtonian counterpart. It is found that the vein's geometric features and the dialysis-induced flow rate have far greater influence on the WSS distribution within the numerical domain.

In the present study, the behaviors of Newtonian and shear-thinning non-Newtonian droplets impinging on heated hydrophilic and hydrophobic surfaces have been investigated numerically using Ansys-Fluent. In this context, the volume-of-fluid technique is applied to track the free-surface of the liquid, and variable time-step is also utilized to control the Courant number. Furthermore, we have considered the dependence of viscosity, density and surface tension on temperature during the simulation. The results are compared to available experimental data at the same conditions, such as boundary conditions. The results demonstrate that there is a good agreement between the obtained results and the experimental trends, concerning normalized diameter profiles at various Weber numbers. Therefore, the focus of the present study is an assessment of the effects of variations in Weber number, contact angle and surface temperature for Newtonian and non-Newtonian liquids on dynamics behavior of droplet in collision with hydrophobic and hydrophilic surfaces. The results represent that the behaviors of Newtonian and non-Newtonian droplets are totally different, indicating the droplet sensitivity to the working parameters.

Detailed knowledge of the blood velocity distribution over the cross-sectional area of a microvessel is important for several reasons: (1) Information about the flow field velocity gradients can suggest an adequate description of blood flow. (2) Transport of blood components is determined by the velocity profiles and the concentration of the cells over the cross-sectional area. (3) The velocity profile is required to investigate volume flow rate as well as wall shear rate and shear stress which are important parameters in describing the interaction between blood cells and the vessel wall. The present study shows the accurate measurement of non-Newtonian blood velocity profiles at different shear rates in a microchannel using a novel translating-stage optical method. Newtonian fluid velocity profile has been well known to be a parabola, but blood is a non-Newtonianfluid which has a plug flow region at the centerline due to yield shear stress and has different viscosities depending on shear rates. The experimental results were compared at the same flow conditions with the theoretical flow equations derived from Casson non-Newtonian viscosity model in a rectangular capillary tube. And accurate wall shear rate and shear stress were estimated for different flow rates based on these velocity profiles. Also the velocity profiles were modeled and compared with parabolic profiles, concluding that the wall shear rates were at least 1.46-3.94 times higher than parabolic distribution for the same volume flow rate.

The volume of fluid (VOF) model is used together with the continuum surface force (CSF) model to numerically simulate the non-Newtonian oil-water core annular flow across return bends. A comprehensive study is conducted to generate the profiles of pressure, velocity, volume fraction and wall shear stress for different oil properties, flow directions, and bend geometries. It is revealed that the oil core may adhere to the bend wall under certain operating conditions. Through the analysis of the total pressure gradient and fouling angle, suitable bend geometric parameters are identified for avoiding the risk of fouling.

A viscous fingering of non-Newtonianfluids at a finite viscosity ratio is considered in order to study the effect of non-Newtonianfluid on crossover phenomena. The crossover from the fractal pattern to the dense structure is investigated by using a two-parameter position-space renormalization-group method. The global flow diagrams in two-parameter space are obtained. It is found that there are two nontrivial fixed points: the fractal point and the Eden point. When the viscosity ratio is finite, the pattern must eventually cross over to the dense structure. The dependences of the crossover phenomena on the parameter k, which describes the different non-Newtonianfluids, are shown. It is found that the non-Newtonianfluids have important effects on the fractal point and the crossover line but the crossover exponent is independent of the non-Newtonian property.

A study on the effects of Navier slip, in conjunction with other flow parameters, on unsteady flow of reactive variable viscosity third-grade fluid through a porous saturated medium with asymmetric convective boundary conditions is presented. The channel walls are assumed to be subjected to asymmetric convective heat exchange with the ambient, and exothermic chemical reactions take place within the flow system. The heat exchange with the ambient obeys Newton’s law of cooling. The coupled equations, arising from the law of conservation of momentum and the first law of thermodynamics, then the derived system are non- dimensionalised and solved using a semi-implicit finite difference scheme. The lower wall slip parameter is observed to increase the fluid velocity profiles, whereas the upper wall slip parameter retards them because of backflow at the upper channel wall. Heat pro- duction in the fluid is seen to increase with the slip parameters. The wall shear stress increases with the slip parameters while the wall heat transfer rate is largely unaltered by the lower wall slip parameter but marginally increased by the upper wall slip parameter.

Although image-based methods like MRI are well-developed, numerical simulation can help to understand human heart function. This function results from a complex interplay of biochemistry, structural mechanics, and blood flow. The complexity of the entire system often causes one of the three parts to be neglected, which limits the truth to reality of the reduced model. This paper focuses on the interaction of myocardial stress distribution and ventricular blood flow during diastole and systole in comparison to a simulation of the same patient-specific geometry with a given wall movement (Spiegel, Strömungsmechanischer Beitrag zur Planung von Herzoperationen, 2009). The orthotropic constitutive law proposed by Holzapfel et al. (Philos. Trans. R. Soc. Lond. Ser. A, 367:3445-3475, 2009) was implemented in a finite element package to model the passive behavior of the myocardium. Then, this law was modified for contraction. Via the ALE method, the structural model was coupled to a flow model which incorporates blood rheology and the circulatory system (Oertel, Prandtl-Essentials of Fluid Mechanics, 3rd edn, Springer Science + Business Media, 2010; Oertel et al., Modelling the Human Cardiac Fluid Mechanics, 3rd edn, Universitätsverlag Karlsruhe, 2009). Comparison reveals a good quantitative and qualitative agreement with respect to fluid flow. The motion of the myocardium is consistent with physiological observations. The calculated stresses and the distribution are within the physiological range and appear to be reasonable. The coupled model presented contains many features essential to cardiac function. It is possible to calculate wall stresses as well as the characteristic ventricular fluid flow. Based on the simulations we derive two characteristics to assess the health state quantitatively including solid and fluid mechanical aspects.

Both clinical and post mortem studies indicate that, in humans, the carotid sinus of the carotid artery bifurcation is one of the favored sites for the genesis and development of atherosclerotic lesions. Hemodynamic factors have been suggested to be important in atherogenesis. To understand the correlation between atherogenesis and fluid dynamics in the carotid sinus, the blood flow in artery was simulated numerically. In those studies, the property of blood was treated as an incompressible, Newtonian fluid. In fact, however, the blood is a complicated non-Newtonianfluid with shear thinning and viscoelastic properties, especially when the shear rate is low. A variety of non-Newtonian models have been applied in the numerical studies. Among them, the Casson equation was widely used. However, the Casson equation agrees well only when the shear rate is less than 10 s-1. The flow field of the carotid bifurcation usually covers a wide range of shear rate. We therefore believe that it may not be sufficient to describe the property of blood only using the Casson equation in the whole flow field of the carotid bifurcation. In the present study, three different blood constitutive models, namely, the Newtonian, the Casson and the hybrid fluid constitutive models were used in the flow simulation of the human carotid bifurcation. The results were compared among the three models. The results showed that the Newtonian model and the hybrid model had very similar distributions of the axial velocity, secondary flow and wall shear stress, but the Casson model resulted in significant differences in these distributions from the other two models. This study suggests that it is not appropriate to only use the Casson equation to simulate the whole flow field of the carotid bifurcation, and on the other hand, Newtonian fluid is a good approximation to blood for flow simulations in the carotid artery bifurcation.

Both clinical and post mortem studies indicate that, in humans, the carotid sinus of the carotid artery bifurcation is one of the favored sites for the genesis and development of atherosclerotic lesions. Hemodynamic factors have been suggested to be important in atherogenesis. To understand the correlation between atherogenesis and fluid dynamics in the carotid sinus, the blood flow in artery was simulated numerically. In those studies, the property of blood was treated as an incompressible, Newtonian fluid. In fact,however, the blood is a complicated non-Newtonianfluid with shear thinning and viscoelastic properties, especially when the shear rate is low. A variety of non-Newtonian models have been applied in the numerical studies. Among them,the Casson equation was widely used. However, the Casson equation agrees well only when the shear rate is less than 10s-1. The flow field of the carotid bifurcation usually covers a wide range of shear rate. We therefore believe that it may not be sufficient to describe the property of blood only using the Casson equation in the whole flow field of the carotid bifurcation. In the present study, three different blood constitutive models, namely, the Newtonian, the Casson and the hybrid fluid constitutive models were used in the flow simulation of the human carotid bifurcation. The results were compared among the three models. The results showed that the Newtonian model and the hybrid model had very similar distributions of the axial velocity, secondary flow and wall shear stress, but the Casson model resulted in significant differences in these distributions from the other two models. This study suggests that it is not appropriate to only use the Casson equation to simulate the whole flow field of the carotid bifurcation, and on the other hand, Newtonian fluid is a good approximation to blood for flow simulations in the carotid artery bifurcation.

Full Text Available We have compared the formation of oil drops in Newtonian and non-Newtonianfluids in a T-junction microfluidic device. As Newtonian fluids, we used aqueous solutions of glycerol, while as non-Newtonianfluids we prepared aqueous solutions of xanthan, a stiff rod-like polysaccharide, which exhibit strong shear-thinning effects. In the squeezing regime, the formation of oil droplets in glycerol solutions is found to scale with the ratio of the dispersed flow rate to the continuous one and with the capillary number associated to the continuous phase. Switching to xanthan solutions does not seem to significantly alter the droplet formation process. Any quantitative difference with respect to the Newtonian liquid can be accounted for by a suitable choice of the capillary number, corresponding to an effective xanthan viscosity that depends on the flow rates. We have deduced ample variations in the viscosity, on the order of 10 and more, during normal operation conditions of the T-junction. This allowed estimating the actual shear rates experienced by the xanthan solutions, which go from tens to hundreds of s−1.

Squire's theorem, which states that the two-dimensional instabilities are more dangerous than the three-dimensional instabilities, is revisited here for a flow down an incline, making use of numerical stability analysis and Squire relationships when available. For flows down inclined planes, one of these Squire relationships involves the slopes of the inclines. This means that the Reynolds number associated with a two-dimensional wave can be shown to be smaller than that for an oblique wave, but this oblique wave being obtained for a larger slope. Physically speaking, this prevents the possibility to directly compare the thresholds at a given slope. The goal of the paper is then to reach a conclusion about the predominance or not of two-dimensional instabilities at a given slope, which is of practical interest for industrial or environmental applications. For a Newtonian fluid, it is shown that, for a given slope, oblique wave instabilities are never the dominant instabilities. Both the Squire relationships and the particular variations of the two-dimensional wave critical curve with regard to the inclination angle are involved in the proof of this result. For a generalized Newtonian fluid, a similar result can only be obtained for a reduced stability problem where some term connected to the perturbation of viscosity is neglected. For the general stability problem, however, no Squire relationships can be derived and the numerical stability results show that the thresholds for oblique waves can be smaller than the thresholds for two-dimensional waves at a given slope, particularly for large obliquity angles and strong shear-thinning behaviors. The conclusion is then completely different in that case: the dominant instability for a generalized Newtonian fluid flowing down an inclined plane with a given slope can be three dimensional.

Full Text Available The hydrodynamic bearings are stressed by severe workings conditions, such as speed, load, and the oil will be increasingly solicit by pressure and shear. The Newtonian behavior is far from being awarded in this case, the most loaded bearings operating at very high speeds; the shear rate of the oil is of higher order. A numerical analysis of the behavior of non-Newtonianfluid for plain cylindrical journal bearing finite dimension coated with antifriction material with a high tin content, for to facilitate the accommodation of the surfaces and save the silk of the shaft in the case of a contact. this analyses is implemented using the code-ANSYS CFX, by solving the energy equation with the finite difference method, considering that laminar regime and the fluid is nonNewtonian by using the power law Ostwald model, the coefficient n is equal to 1.25 and for different model such as Bingham, cross and Hereshek-Bulkley model. This study aims to better predict the non-Newtonian behavior of the oil film in bearings operating under more severe conditions. The purpose conducted during this study is to predict the effect of non-Newtonian behavior of the film; the journal bearing operating under severe conditions, the speed of rotation varies from 1000 to 9000 rpm and the bearing working under radial load 2 to 10 kN. Temperature and the pressure within the fluid film assumed non-Newtonian are high, with a coefficient n greater than 1 that is to say for viscoelastic fluids.

Non-Newtonianfluids are extensively used in enhanced oil recovery. However, understanding the flow of such fluids in complex porous media remains a challenging problem. In the presented study, we use computational fluid dynamics to investigate the creeping flow of a particular non-Newtonianfluid through porous media, namely a power-law fluid with a newtonian behavior below a critical shear rate. We show that the nonlinear effects induced by the rheology only weakly impact the topological st...

The present work on downward injection of non-Newtonian jet is an extension of our recent work (Lakdawala et al, Int. J. Multiphase Flow. 59: 206–220, 2014) on upward injection of Newtonian jet. The non-Newtonian rheology of the jet is described by a Carreau type generalized Newtonian fluid (GNF) model, which is a phenomenological constitutive equation that accounts for both rate-thinning and rate-thickening. Level set method based numerical study is done for Newtonian as well as various types of shear thinning and thickening jet fluid. Effect of average injection velocity ($V_{av,i}$) is studied at a constant Reynolds number Re = 14.15, Weber number W e = 1, Froude number F r = 0.25, density ratio $\\chi$ = 0.001 and viscosity ratio $\\eta$ = 0.01. CFD analysis of the temporal variation of interface and jet length ($L_{j}$) is done to propose different types of jet breakup regimes. At smaller, intermediate and larger values of $V_{av,i}$, the regimes found are periodic uniform drop (P-UD), quasi-periodic non-uniform drop (QP-NUD) and no breakup (NB) regimes for a shear thinning jet; and periodic along with Satellite Drop (P+S), jetting (J) and no breakup (NB) regimes for a shear thickening jet, respectively. This is presented as a drop-formation regime map. Shear thickening (thinning) is shown to produce long (short) jet length. Diameter of the primary drop increases and its frequency of release decreases, due to increase in stability of the jet for shear thickening as compared to thinning fluid.

Full Text Available Background: There is considerable evidence that vascular fluid dynamics plays an important role in the developmentand prevalence of atherosclerosis which is one of the most widespread disease in humans .The onset and prevalence of atherosclerosis hemodynamic parameter are largely affected by geometric parameters. If any obstacle interferes with the blood flow, the above parameters change dramatically. Most of the arterial diseases, such as atherosclerosis, occur in the arteries with complex patterns of fluid flow where the blood dynamics plays an important role. Arterial stenosis mostly occurs in an area with a complex pattern of fluid flow, such as coronary artery, aorta bifurcation, carotid and vessels of lower limbs. During the past three decades, many experimental studies have been performed on the hemodynamic role of the blood in forming sediment in the inner wall of the vessels. It has been shown that forming sediment in the inner wall of vessels depends on the velocity of fluid and also on the amount of wall shear stress.Methods: We have examined the effect on the blood flow of local stenosis in carotid artery in numerical form using the incompressible Navier-Stockes equations. The profile of the velocity in different parts and times in the pulsatile cycle, separation and reattachment points on the wall, the distance stability of flow and also alteration caused by the wall shear stress in entire vessel were shown and compared with two behaviors flow (Newtonian and Non-Newtonian.Finally we describe the influence of the severity of the stenosis on the separation and reattachmentpoints for a Non-Newtonian fuid. Results: In the present study, we have pointed very low and high oscillating WSS (Wall Shear Stress values play a significant role in the development of forming sediment in the inner wall of vessels. Also, we obtain this probability is higher for Newtonian than Non-Newtonianfluid behavior.Conclusion: Based on our results, the

Full Text Available Abstract The rheological behaviour of ethylene glycol-based nanofluids containing hexagonal scalenohedral-shaped α-Fe2O3 (hematite nanoparticles at 303.15 K and particle weight concentrations up to 25% has been carried out using a cone-plate Physica MCR rheometer. The tests performed show that the studied nanofluids present non-Newtonianshear-thinning behaviour. In addition, the viscosity at a given shear rate is time dependent, i.e. the fluid is thixotropic. Finally, using strain sweep and frequency sweep tests, the storage modulus G', loss modulus G″ and damping factor were determined as a function of the frequency showing viscoelastic behaviour for all samples.

The rheology of many heavy oils has been shown to be non-Newtonian, Bingham plastics being one manifestation of heavy oil flow. In EOR applications, non-Newtonianfluids such as low concentration polymer solutions, emulsions, gels etc. are simultaneously injected to increase the viscosity of driving agents that displace oil. Such rheologically complex fluids are used to improve sweep efficiencies, divert displacing fluids and block swept zones. The present study has been undertaken to understand the flow of non-Newtonianfluids through porous media. The work considered involves the numerical (pore network) modeling of both single and multiphase flow of power-law and Bingham plastic fluids in network-like porous media. We consider aspects of both single- and multi-phase flow and displacement. Section 2 describes elementary aspects of non-Newtonian flow and some simple models for porous media. Viscoelastic effects in the flow of non-Newtonianfluids are also discussed. The section includes a brief literature review on non-Newtonian flow in porous media. Section 3 describes single-phase flow.

The inks used in gravure-offset printing are non-Newtonianfluids with higher viscosities and lower surface tensions than Newtonian fluids. This paper examines the transfer of a non-Newtonian ink between a flat plate and a groove when the plate is moved upward with a constant velocity while the groove is held fixed. Numerical simulations were carried out with the Carreau model to explore the behavior of this non-Newtonian ink in gravure-offset printing. The volume of fluid (VOF) method was implemented to capture the interface during the ink transfer process. The effects of varying the contact angle of the ink on the flat plate and groove walls and geometrical parameters such as the groove angle and the groove depth on the breakup time of the liquid filament that forms between the plate and the groove and the ink transfer ratio were determined. Our results indicate that increasing the groove contact angle and decreasing the flat plate contact angle enhance the ink transfer ratio and the breakup time. However, increasing the groove depth and the groove angle decreases the transfer ratio and the breakup time. By optimizing these parameters, it is possible to achieve an ink transfer from the groove to the flat plate of approximately 92%. Moreover, the initial width and the vertical velocity of the neck of the ink filament have significant influences on the ink transfer ratio and the breakup time.

Many volcanoes exhibit temporal changes in their degassing process, from rapid gas puffing to lava fountaining and long-lasting quiescent passive degassing periods. This range of behaviors has been explained in terms of changes in gas flux and/or magma input rate. We report here a simple laboratory experiment which shows that the non- Newtonian rheology of magma can be responsible, alone, for such intriguing behavior, even in a stationary gas flux regime. We inject a constant gas flow-rate Q at the bottom of a non-Newtonianfluid column, and demonstrate the existence of a critical flow rate Q* above which the system spontaneously alternates between a bubbling and a channeling regime, where a gas channel crosses the entire fluid column. The threshold Q* depends on the fluid rheological properties which are controlled, in particular, by the gas volume fraction (or void fraction) {\\phi}. When {\\phi} increases, Q* decreases and the degassing regime changes. Non-Newtonian properties of magma might therefore play a...

The problem of the effect of Joule heating generation on the hydrodynamic profile and the solute transport found in electrophoretic devices is addressed in this article. The research is focused on the following two problems: The first one is centered around the effect of Joule heating on the hydrodynamic velocity profile and it is referred to as "the carrier fluid problem." The other one is related to the effect of Joule heating on the solute transport inside electrophoretic cells and it is r...

This paper is concerned with time decay rates for weak solutions to a class system of isotropic incompressible non-Newtonianfluid motion in Rn. With the use of the spectral decomposition methods of Stokes operator, the optimal decay estimates of weak solutions in L2 norm are derived under the different conditions on the initial velocity. Moreover, the error estimates of the difference between non-Newtonian flow and Navier-Stokes flow are also investigated.

Full Text Available The peristaltic motion of a third order fluid due to asymmetric waves propagating on the sidewalls of a inclined asymmetric channel is discussed. The key features of the problem includes longwavelength and low-Reynolds number assumptions. A mathematical analysis has been carried out to investigate the effect of slip condition, variable viscosity and magnetohydrodynamics (MHD. Followed by the nondimensionalization of the nonlinear governing equations along with the nonlinear boundary conditions, a perturbation analysis is made. For the validity of the approximate solution, a numerical solution is obtained using the iterative collocation technique.

The flow of blood in narrow arteries with bell-shaped mild stenosis is investigated that treats blood as non-Newtonianfluid by using the K-L model. When skin friction and resistance of blood flow are normalized with respect to non-Newtonian blood in normal artery, the results present the effect of stenosis length. When skin friction and resistance of blood flow are normalized with respect to Newtonian blood in stenosis artery, the results present the effect of non-Newtonian blood. The effect of stenosis length and effect of non-Newtonianfluid on skin friction are consistent with the Casson model in which the skin friction increases with the increase of either stenosis length or the yield stress but the skin friction decreases with the increase of plasma viscosity coefficient. The effect of stenosis length and effect of non-Newtonianfluid on resistance of blood flow are contradictory. The resistance of blood flow (when normalized by non-Newtonian blood in normal artery) increases when either the plasma viscosity coefficient or the yield stress increases, but it decreases with the increase of stenosis length. The resistance of blood flow (when normalized by Newtonian blood in stenosis artery) decreases when either the plasma viscosity coefficient or the yield stress increases, but it decreases with the increase of stenosis length.

We consider, for the first time, the stability of the non-Newtonian boundary layer flow over a flat plate. Shear-thinning and shear-thickening flows are modelled using a Carreau constitutive viscosity relationship. The boundary layer equations are solved in a self-similar fashion. A linear asymptotic stability analysis, that concerns the lower-branch structure of the neutral curve, is presented in the limit of large Reynolds number. It is shown that the lower-branch mode is destabilised and stabilised for shear-thinning and shear-thickening fluids, respectively. Favourable agreement is obtained between these asymptotic predictions and numerical results obtained from an equivalent Orr-Sommerfeld type analysis. Our results indicate that an increase in shear-thinning has the effect of significantly reducing the value of the critical Reynolds number, this suggests that the onset of instability will be significantly advanced in this case. This postulation, that shear-thinning destabilises the boundary layer flow, is further supported by our calculations regarding the development of the streamwise eigenfunctions and the relative magnitude of the temporal growth rates.

Full Text Available In this article, we investigate the nonlinear steady boundary layer flow and heat transfer of an incompressible Tangent Hyperbolic fluid from a sphere. The transformed conservation equations are solved numerically subject to physically appropriate boundary conditions using implicit finite-difference Keller Box technique. The numerical code is validated with previous studies. The influence of a number of emerging non-dimensional parameters, namely Weissenberg number (We, power law index (n, Prandtl number (Pr, Biot number (γ and dimensionless tangential coordinate (ξ on velocity and temperature evolution in the boundary layer regime is examined in detail. Furthermore, the effects of these parameters on heat transfer rate and skin friction are also investigated. Validation with earlier Newtonian studies is presented and excellent correlation is achieved. It is found that the velocity, Skin friction and the Nusselt number (heat transfer rate are decreased with increasing Weissenberg number (We, whereas the temperature is increased. Increasing power law index (n increases the velocity and the Nusselt number (heat transfer rate but decreases the temperature and the Skin friction. An increase in the Biot number (γ is observed to increase velocity, temperature, local skin friction and Nusselt number. The study is relevant to chemical materials processing applications.

The spiral component of blood flow has both beneficial and detrimental effects in human circulatory system. A numerical investigation is carried out to analyze the effects of spiral blood flow through an axisymmetric three dimensional artery having 75% stenosis at the center. Blood is assumed as a non-Newtonianfluid. Standard k-ω model is used for the simulation with the Reynolds number of 1000. A parabolic velocity profile with spiral flow is used as inlet boundary condition. The peak values of all velocity components are found just after stenosis. But total pressure gradually decreases at downstream. Spiral flow of blood has significant effects on tangential component of velocity. However, the effect is mild for radial and axial velocity components. The peak value of wall shear stress is at the stenosis zone and decreases rapidly in downstream. The effect of spiral flow is significant for turbulent kinetic energy. Detailed investigation and relevant pathological issues are delineated throughout the paper.

Monodispersity and fast generation are innate advantages of microfluidic droplets. Other than the normally adopted simple Newtonian fluids such as a water/oil emulsion system, fluids with complex rheology, namely, non-Newtonianfluids, which are being widely adopted in industries and bioengineering, have gained increasing research interest on the microscale. However, challenges occur in controlling the dynamic behavior due to their complex properties. In this sense, the AC electric field with merits of fast response and easiness in fulfilling "Lab on a chip" has attracted our attention. We design and fabricate flow-focusing microchannels with non-contact types of electrodes for the investigation. We firstly compare the formation of a non-Newtonian droplet with that of a Newtonian one under an AC electric field and discover that viscoelasticity contributes to the discrepancies significantly. Then we explore the effect of AC electric fields on the filament thinning and droplet formation dynamics of one non-Newtonianfluid which has a similar rheological behavior to bio samples, such as DNA or blood samples. We investigate the dynamics of the thinning process of the non-Newtonian filament under the influence of an AC electric field and implement a systematic exploration of the non-Newtonian droplet generation influenced by parameters such as the flow conditions (flow rate Q, capillary number Ca), fluid property (Weissenberg number Wi), applied voltage (U) and frequency (f) of the AC electric field. We present the dependencies of the flow condition and electric field on the non-Newtonian droplet formation dynamics, and conclude with an operating diagram, taking into consideration all the above-mentioned parameters. Results show that the electric field plays a critical role in controlling the thinning process of the filament and the size of the generated droplet. Furthermore, for the first time, we quantitatively measure the flow field of the non-Newtonian droplet

Considerations on implementation of the stress-strain constitutive relations applied in Computational Fluid dynamics (CFD) simulation of cardiovascular flows have been addressed extensively in the literature. However, the matter is yet controversial. The author suggests that the choice of non-Newtonian models and the consideration of non-Newtonian assumption versus the Newtonian assumption is very application oriented and cannot be solely dependent on the vessel size. In the presented work, where a renal disease patient-specific geometry is used, the non-Newtonian effects manifest insignificant, while the vessel is considered to be medium to small which, according to the literature, suggest a strict use of non-Newtonian formulation. The insignificance of the non-Newtonian effects specially manifests in Wall Shear Stress (WSS) along the walls of the numerical domain, where the differences between Newtonian calculated WSS and non-Newtonian calculated WSS is barely visible.

The flow curvesshear-rate rangeby using theof bagasse Kraft black liquor over aof 10-1 s- 1-103s- 1 were investigatedRheometric RFSII rheometerExperimental results show that Bagasse black liquorsare non-Newtonianfluids instead of Newtonian fluidsat higher solids contents, and the viscosities of blackliquor would decrease about 2-3 orders of magnitudewith an increase in the shear rates. The apparentviscosity and flow behavior of bagasse black liquorare also affected by its solids content, and the highersolids content the more shear-thinning bagasse blackliquor fluid is. In addition, the power-law equationwas utilized to fit these flow curves at differentconditions. Finally, the significances ofshear-thinning properties of bagasse black liquor inthe chemical recovery system, such as frictioncalculation of pipe and design optimization of thewhole recovery system, were presented.

We have recently developed a novel design for coronary arterial bypass surgical grafting, consisting of coupled sequential side-to-side and end-to-side anastomoses. This design has been shown to have beneficial blood flow patterns and wall shear stress distributions which may improve the patency of the CABG, as compared to the conventional end-to-side anastomosis. In our preliminary computational simulation of blood flow of this coupled sequential anastomoses design, the graft and the artery were adopted to be rigid vessels and the blood was assumed to be a Newtonian fluid. Therefore, the present study has been carried out in order to (i) investigate the effects of wall compliance and non-Newtonian rheology on the local flow field and hemodynamic parameters distribution, and (ii) verify the advantages of the CABG coupled sequential anastomoses design over the conventional end-to-side configuration in a more realistic bio-mechanical condition. For this purpose, a two-way fluid-structure interaction analysis has been carried out. A finite volume method is applied to solve the three-dimensional, time-dependent, laminar flow of the incompressible, non-Newtonianfluid; the vessel wall is modeled as a linearly elastic, geometrically non-linear shell structure. In an iteratively coupled approach the transient shell equations and the governing fluid equations are solved numerically. The simulation results indicate a diameter variation ratio of up to 4% and 5% in the graft and the coronary artery, respectively. The velocity patterns and qualitative distribution of wall shear stress parameters in the distensible model do not change significantly compared to the rigid-wall model, despite quite large side-wall deformations in the anastomotic regions. However, less flow separation and reversed flow is observed in the distensible models. The wall compliance reduces the time-averaged wall shear stress up to 32% (on the heel of the conventional end-to-side model) and somewhat

The peculiarities of simple shear flow of shear thinning fluids over a superhydrophobic wall consisting of a set of parallel gas-filled grooves and solid stripes (domains with slip and stick boundary conditions) are studied numerically. The Carreau-Yasuda model is used to provide further insight into the problem of the slip behavior of non-Newtonianfluids having a decreasing viscosity with a shear rate increase. This feature is demonstrated to cause a nonlinear velocity profile leading to the apparent slip. The corresponding transverse and longitudinal apparent slip lengths of a striped texture are found to be noticeably larger than the respective effective slip lengths of Newtonian liquids in microchannels of various thicknesses and surface fractions of the slip domains. The viscosity distribution of the shear thinning fluid over the superhydrophobic wall is carefully investigated to describe the mechanism of the apparent slip. Nonmonotonic behavior of the apparent slip length as a function of the applied shear rate is revealed. This important property of shear thinning fluids is considered to be sensitive to the steepness of the viscosity flow curve, thus providing a way to decrease considerably the flow resistance in microchannels.

An aqueous solution of Xanthan Gum (XG) at a weight fraction as high as 0.2% was used as the base liquid, the stable MWCNTs-dispersed non-Newtonian nanofluids at different weight factions of MWCNTs was prepared. The base fluid and all nanofluids show pseudoplastic (shear-thinning) rheological behavior. Experiments were performed to compare the shell-side forced convective heat transfer coefficient and pressure drop of non-Newtonian nanofluids to those of non-Newtonian base fluid in an integrally helical baffle heat exchanger with low-finned tubes. The experimental results showed that the enhancement of the convective heat transfer coefficient increases with an increase in the Peclet number and the nanoparticle concentration. For nanofluids with 1.0, 0.5 and 0.2 wt% of multi-walled carbon nanotubes (MWCNTs), the heat transfer coefficients respectively augmented by 24.3, 13.2 and 4.7% on average and the pressure drops become larger than those of the base fluid. The comprehensive thermal performance factor is higher than one and increases with an increasing weight fraction of MWCNTs. A remarkable heat transfer enhancement in the shell side of helical baffle heat exchanger with low-finned tubes can be obtained by adding MWCNTs into XG aqueous solution based on thermal resistance analysis. New correlations have been suggested for the shell-side friction coefficient and the Nusselt numbers of non-Newtonian nanofluids and give very good agreement with experimental data.

Classical particles oscillating in high-frequency or static fields effectively exhibit a modified rest mass meff which determines the oscillation center motion. Unlike the true mass, meff depends on the field parameters and can be a nonanalytic function of the particle average velocity and the oscillation energy; hence non-Newtonian "metaplasmas" that permit a new type of plasma maser, signal rectification, frequency doubling, and one-way walls.

This paper studies power-law non-Newtonianfluid where the shearing stress accords with the Ostwald-de Waele relational formula.It aims to solve the problem of the apparent viscosity changing with the shearing rates and the calculation which is different from Newtonian fluid.Cell-based central method is used for the non-linear viscosity coefficient discretization.It adopts FVM for flow and heat transfer numerical simulation of fully developed laminar in eccentric annular channel.The calculation results show that the power-law factor has a great impact on the fluid flow,but the impact on the heat transfer is influenced by the eccentricity .The eccentric-ity of annular channel can lead to the asymmetrical distribution of circumferential temperature and velocity.%以剪切应力符合Ostwald-de Waele关系式的幂律非牛顿流体为研究对象。针对幂律非牛顿流体的表观黏度随剪切速率变化且计算过程有别于牛顿流体的问题，运用基元中心法对非线性粘性系数进行离散。采用有限体积法对幂律非牛顿流体在偏心圆环管中的充分发展层流流动和传热进行数值计算。计算结果表明流体的幂律因子对流动的影响较大，但对传热的影响受到到偏心率的影响。流道偏心会引起圆环通道内速度和温度的周向分布不均匀，且偏心程度越严重，周向分布不均匀性越强烈。

When a fluid jet impinges on a solid substrate, a variety of behaviors may occur around the impact region. One example is mounding, where the fluid enters the impact region faster than it can flow away, forming a mound of fluid above the main surface. For some operating conditions, this mound can destabilize and buckle, entraining air in the mound. Other behaviors include submerging flow, where the jet impinges into an otherwise steady pool of liquid, entraining a thin air layer as it enters the pool. This impact region is one of very high shear rates and as such, complex fluids behave very differently than do Newtonian fluids. In this work, we attempt to characterize this range of behavior for Newtonian and non-Newtonianfluids using dimensionless parameters. We model the fluid as a modified Bingham-Carreau-Yasuda fluid, which exhibits the full range of pseudoplastic flow properties throughout the impact region. Additionally, we study viscoelastic effects through the use of the Giesekus model. Both 2-D and 3-D numerical simulations are performed using a variety of finite element method techniques for tracking the jet interface, including Arbitrary Lagrangian Eulerian (ALE), diffuse level sets, and a conformal decomposition finite element method (CDFEM). The presence of shear-thinning characteristics drastically reduces unstable mounding behavior, yet can lead to air entrainment through the submerging flow regime. We construct an operating map to understand for what flow parameters mounding and submerging flows will occur, and how the fluid rheology affects these behaviors. This study has many implications in high-speed industrial bottle filling applications.

Full Text Available This work applies a fractional flow model to describe a time-variant behavior of non-Newtonian substances. Specifically, we model the physical mechanism underlying the thixotropic and anti-thixotropic phenomena of non-Newtonian flow. This study investigates the behaviors of cellulose suspensions and SMS pastes under constant shear rate. The results imply that the presented model with only two parameters is adequate to fit experimental data. Moreover, the parameter of fractional order is an appropriate index to characterize the state of given substances. Its value indicates the extent of thixotropy and anti-thixotropy with positive and negative order respectively.

Full Text Available This paper presents theoretical investigations of rheological effects of lubricant on stability parameters of various configurations of slot-entry hybrid journal bearing system. FEM has been used to solve Reynolds equation governing flow of lubricant in bearing clearance space along with restrictor flow equation using suitable iterative technique. The non-Newtonian lubricant has been assumed to follow cubic shear stress law. The stability parameters in terms of stiffness coefficients, damping coefficients, threshold speed and whirl frequency of different configurations of slot-entry hybrid journal bearing have been computed and presented for wide range of external load while operating with Newtonian and Non-Newtonian lubricants. The computed results reveal that variation of viscosity due to non-Newtonian behavior of lubricant affects bearing stability quite significantly. The results are presented in graphical form and logical conclusions are drawn to identify best possible configuration from stability point of view.

Full Text Available The quartz crystal microbalance (QCM is increasingly used for monitoring the interfacial interaction between surfaces and macromolecules such as biomaterials, polymers, and metals. Recent QCM applications deal with several types of liquids with various viscous macromolecule compounds, which behave differently from Newtonian liquids. To properly monitor such interactions, it is crucial to understand the influence of the non-Newtonianfluid on the QCM measurement response. As a quantitative indicator of non-Newtonian behavior, we used the quartz resonator signature, S2, of the QCM measurement response, which has a consistent value for Newtonian fluids. We then modified De Kee’s non-Newtonian three-parameter model to apply it to our prediction of S2 values for non-Newtonian liquids. As a model, we chose polyethylene glycol (PEG400 with the titration of its volume concentration in deionized water. As the volume concentration of PEG400 increased, the S2 value decreased, confirming that the modified De Kee’s three-parameter model can predict the change in S2 value. Collectively, the findings presented herein enable the application of the quartz resonator signature, S2, to verify QCM measurement analysis in relation to a wide range of experimental subjects that may exhibit non-Newtonian behavior, including polymers and biomaterials.

Full Text Available Smart materials of magnetorheological (MR fluids could be turned from a liquid state into a solid state, which solidification extent or shear strength often increases monotonically with the applied magnetic field. In this study, the shear stress of a dilute MR fluid decreased with increasing applied magnetic field at a constant shear rate. The dynamic shear stress was significantly higher than the stable counterpart at medium magnetic fields. They are ascribed to the slow particle structure transformation. A higher shear rate and particle volume fraction could reduce the transient time and the shear strength difference.

Viscous fingering in non-Newtonianfluids in a rectangular Hele-Shaw cell was investigated. The cell was filled with a 0.5 or 1.0wt% aqueous solution of carboxymethylcellulose (CMC), a shear-thinning fluid. Air was injected into the cell and the growth of viscous fingers was observed. The velocity of finger tip was characterized by the pressure gradient. A modified Darcy law was able to describe the characteristics of the tip velocity that the growth rate of the tip velocity increased with increasing pressure gradient in the CMC solutions. The prediction of tip velocity with the modified Darcy law indicated that an effective pressure gradient near the tip was larger than the average pressure gradient between the finger tip and the cell exit and that the rate of increase depended on the cell gap width.

To illustrate the behavior of polymeric fluids and in what respects they differ from Newtonian liquids, an experiment was developed to account for the shear-rate dependence of non-Newtonianfluids. Background information, procedures, and results are provided for the experiment. Useful in transport processes, fluid mechanics, or physical chemistry…

在一个轴对称、外形任意的多孔介质二维体中,充满了有屈服应力的非Newton幂律流体时,数值分析其自由对流及其传热/传质问题,利用相似变换,将边界层控制方程及其边界条件变换为无量纲形式,然后用有限差分法求解该方程组.所研究的参数为流变常数、浮力比和Lewis数.给出并讨论了典型的速度、温度及浓度曲线,发现屈服应力参数值和非Newton流体的幂律指数对结果有着显著的影响.%Numerical analysis of free convection coupled heat and mass transfer was presented for non-Newtonian power-law fluids with yield stress flowing over two-dimensional or axisymmetric body of arbitrary shape in a fluid-saturated porous medium.The governing boundary layer equations and boundary conditions were cast into a dimensionless form by similarity transformation and the resulting system of equations was solved by a finite difference method.The parameters studied were the rheologicai constants, the buoyancy ratio, and the Lewis number.Representative velocity as well as temperature and concentration profiles were presented and discussed.It was found that the result depend strongly on the values of the yield stress parameter, and the power-law index of non-Newtonianfluid.

This paper presents a new theory of turbulent mixing in stirred reactors. The degree of homogeneity of a mixed fluid may be characterized by the Kolmogorov micro-scale. The smaller its value, the better homogeneity. The micro-scale scales inversely with the fourth root of the energy dissipation rate in the stirring process. The higher this rate, the smaller lambda, and the better the homogeneity in the reactor. This is true for Newtonian fluids. In non-Newtonianfluids the situation is different. For instance, in shear-thickening fluids it is plausible that high shear rates thicken the fluid and might strangle the mixing. The internal interactions between different fluid-mechanical and colloidal variables are subtle, namely due to the (until recently) very limited understanding of turbulence. Starting from a qualitatively new turbulence theory for inviscid fluids [Baumert, 2013], giving e.g. the Karman constant as $(2\\pi)^{-1/2} = 0.40$ [the super-pipe in Princeton gave 0.40 p/m 0.02, Bailey et al., 2014], we...

The Virtual Intracranial Stenting Challenge 2007 (VISC'07) is becoming a standard test case in computational minimally invasive cerebrovascular intervention. Following views expressed in the literature and consistent with the recommendations of a report, the effects of non-Newtonian viscosity and pulsatile flow are reported. Three models of stented cerebral aneurysms, originating from VISC'07 are meshed and the flow characteristics simulated using commercial computational fluid dynamics (CFD) software. We conclude that non-Newtonian and pulsatile effects are important to include in order to discriminate more effectively between stent designs.

Shear thickening is a non-Newtonianfluid behavior defined as the increase of viscosity with the increase in the applied shear rate. The shear thickening fluid (STF) is a combination of hard metal oxide particles suspended in a liquid polymer. This mixture of flowable and hard components at a particular composition, results in a material with remarkable properties. In this manuscript the shear thickening fluid (STF) was prepared by ultrasound irradiation of silica nanoparticles dispersed in liquid polyethylene glycol polymer. The as-prepared STFs have been tested for their rheological and thermal properties. Kevlar and Nylon fabrics were soaked in STF/ethanol solution to make STF/fabric composite. Knife threats and quasistatic penetration tests were performed on the neat fabrics and STF/fabric composite targets for both engineered spike and knife on areal density basis. The results showed that STF impregnated fabrics have better penetration resistance as compared to neat fabrics without affecting the fabric flexibility. This indicates that the addition of STF to the fabric have enhanced the fabric performance and can be used in liquid body armor applications.

All families of inorganic glass-forming liquids display non-Newtonian rheological behavior in the form of shear thinning at high shear rates. Experimental evidence is presented to demonstrate the existence of remarkable universality in this behavior, irrespective of chemical composition, structure, topology, and viscosity. However, contrary to intuition, in all cases the characteristic shear rates that mark the onset of shear thinning in these liquids are orders of magnitude slower than the global shear relaxation rates. Attempt is made to reconcile such differences within the framework of the cooperative structural relaxation model of glass-forming liquids.

A simple experiment designed to study mixing of a material of complex rheology in a stirred tank is described. Non-Newtonian suspensions of blue maize flour that naturally contain anthocyanins have been chosen as a model fluid. These anthocyanins act as a native, wide spectrum pH indicator exhibiting greenish colors in alkaline environments, blue…

A small scale isotropic mass transfer model was developed for the local liquid side mass transfer coefficients in gas-liquid-solid three-phase flow airlift loop reactor for Newtonian and non-Newtonianfluids.It is based on Higbie's penetration theory and Kolmogoroff's theory of isotropic turbulence with k1 = 3√2Dε1/3 1/π(η-1/3 1 -λ-1/3 f),where ε1 is local rate of energy dissipation,λf is the local microscale,η1 is the local Kolmogoroff scale and D is the diffusion coefficient.The capability of the proposed model is discussed in the light of experimental data obtained from 12 L gas-liquid-solid three-phase flow airlift loop reactor using Newtonian and non-Newtonianfluids.Good agreement with the experimental data was obtained over a wide range of conditions suggesting a general applicability of the proposed model.

A thermal elastohydrodynamic lubrication (TEHL)finite line contact model was proposed for a cylindrical roller with Ree-Eyring fluid and Power-Law fluid.The results show that with the increase of contact line length,end effect is decreased.The Eyring shear stress for Ree-Eyring fluid has a great influence on the temperature rise and shear stress, while has a little influence on the pressure and film thickness.For Power-Law fluid,the film thickness is decreased dramat-ically with the increase of Power-Law exponent.Compared with the isothermal results,the thermal results are quite different with the increase of load and speed,and there is a more significant influence on friction coefficient for thermal effects.%建立有限长圆柱滚子的非牛顿流体热弹流润滑模型，选取Ree-Eyring流体和Power-Law流体进行有限长线接触弹流润滑分析。研究表明：随着接触线长度增大，端部效应减弱；Ree-Eyring流体特征剪切力对润滑温升和剪切力影响较大，而对润滑压力与膜厚影响甚微；Power-Law流体随指数增大，润滑膜厚明显降低；随载荷、转速升高，热解与等温润滑结果差异增大，热效应对摩擦因数的影响尤其显著。

Full Text Available Flow characteristics and heat transfer performances in rectangular tubes with protrusions are numerically investigated in this paper. The thermal heat transfer enhancement of composite structures and flow resistance reduction of non-Newtonianfluid are taken advantage of to obtain a better thermal performance. Protrusion channels coupled with different CMC concentration solutions are studied, and the results are compared with that of smooth channels with water flow. The comprehensive influence of turbulence effects, structural effects, and secondary flow effects on the CMC’s flow in protrusion tubes is extensively investigated. The results indicate that the variation of flow resistance parameters of shear-thinning power-law fluid often shows a nonmonotonic trend, which is different from that of water. It can be concluded that protrusion structure can effectively enhance the heat transfer of CMC solution with low pressure penalty in specific cases. Moreover, for a specific protrusion structure and a fixed flow velocity, there exists an optimal solution concentration showing the best thermal performance.

Full Text Available Assessment of the potential of a polymer flood for mobility control requires an accurate model on the viscosities of displacement fluids involved in the process. Because most polymers used in EOR exhibit shear-thinning behavior, the effective viscosity of a polymer solution is a highly nonlinear function of shear rate. A reservoir simulator including the model for the shear-rate dependence of viscosity was used to investigate shear-thinning effects of polymer solution on the performance of the layered reservoir in a five-spot pattern operating under polymer flood followed by waterflood. The model can be used as a quantitative tool to evaluate the comparative studies of different polymer flooding scenarios with respect to shear-rate dependence of fluids’ viscosities. Results of cumulative oil recovery and water-oil ratio are presented for parameters of shear-rate dependencies, permeability heterogeneity, and crossflow. The results of this work have proven the importance of taking non-Newtonian behavior of polymer solution into account for the successful evaluation of polymer flood processes. Horizontal and vertical permeabilities of each layer are shown to impact the predicted performance substantially. In reservoirs with a severe permeability contrast between horizontal layers, decrease in oil recovery and sudden increase in WOR are obtained by the low sweep efficiency and early water breakthrough through highly permeable layer, especially for shear-thinning fluids. An increase in the degree of crossflow resulting from sufficient vertical permeability is responsible for the enhanced sweep of the low permeability layers, which results in increased oil recovery. It was observed that a thinning fluid coefficient would increase injectivity significantly from simulations with various injection rates. A thorough understanding of polymer rheology in the reservoir and accurate numerical modeling are of fundamental importance for the exact estimation

Non-Newtonianfluids occur in many relevant flow and mixing scenarios at the lab and industrial scale. The addition of acid or basic solutions to a non-Newtonianfluid is not an infrequent operation, particularly in Biotechnology applications where the pH of Non-Newtonian culture broths is usually regulated using this strategy. We conducted mixing experiments in agitated vessels using Non-Newtonian blue maize flour suspensions. Acid or basic pulses were injected to reveal mixing patterns and flow structures and to follow their time evolution. No foreign pH indicator was used as blue maize flours naturally contain anthocyanins that act as a native, wide spectrum, pH indicator. We describe a novel method to quantitate mixedness and mixing evolution through Dynamic Color Analysis (DCA) in this system. Color readings corresponding to different times and locations within the mixing vessel were taken with a digital camera (or a colorimeter) and translated to the CIELab scale of colors. We use distances in the Lab space, a 3D color space, between a particular mixing state and the final mixing point to characterize segregation/mixing in the system. Blue maize suspensions represent an adequate and flexible model to study mixing (and fluid mechanics in general) in Non-Newtonian suspensions using acid/base tracer injections. Simple strategies based on the evaluation of color distances in the CIELab space (or other scales such as HSB) can be adapted to characterize mixedness and mixing evolution in experiments using blue maize suspensions.

Full Text Available BACKGROUND: Non-Newtonianfluids occur in many relevant flow and mixing scenarios at the lab and industrial scale. The addition of acid or basic solutions to a non-Newtonianfluid is not an infrequent operation, particularly in Biotechnology applications where the pH of Non-Newtonian culture broths is usually regulated using this strategy. METHODOLOGY AND FINDINGS: We conducted mixing experiments in agitated vessels using Non-Newtonian blue maize flour suspensions. Acid or basic pulses were injected to reveal mixing patterns and flow structures and to follow their time evolution. No foreign pH indicator was used as blue maize flours naturally contain anthocyanins that act as a native, wide spectrum, pH indicator. We describe a novel method to quantitate mixedness and mixing evolution through Dynamic Color Analysis (DCA in this system. Color readings corresponding to different times and locations within the mixing vessel were taken with a digital camera (or a colorimeter and translated to the CIELab scale of colors. We use distances in the Lab space, a 3D color space, between a particular mixing state and the final mixing point to characterize segregation/mixing in the system. CONCLUSION AND RELEVANCE: Blue maize suspensions represent an adequate and flexible model to study mixing (and fluid mechanics in general in Non-Newtonian suspensions using acid/base tracer injections. Simple strategies based on the evaluation of color distances in the CIELab space (or other scales such as HSB can be adapted to characterize mixedness and mixing evolution in experiments using blue maize suspensions.

In this study, computational fluid dynamics and the laminar flow of the non-Newtonianfluid have been numerically studied. The cooling fluid includes water and 0.5 wt% Carboxy methyl cellulose (CMC) making the non-Newtonianfluid. In order to make the best of non-Newtonian nanofluid in this simulation, solid nanoparticles of Aluminum Oxide have been added to the non-Newtonianfluid in volume fractions of 0-2% with diameters of 25, 45 and 100 nm. The supposed microchannel is rectangular and two-dimensional in Cartesian coordination. The power law has been used to speculate the dynamic viscosity of the cooling nanofluid. The field of numerical solution is simulated in the Reynolds number range of 5 ribs with angle of attacks of 30°, 45° and 60° is studied on flow parameters and heat transfer due to the fluid flow. The results show that an increase in the volume fraction of nanoparticles as well as the use for nanoparticles with smaller diameters lead to greater heat transfer. Among all the studied forms, the triangular rib from with an angle of attack 30° has the biggest Nusselt number and the smallest pressure drop along the microchannel. Also, an increase in the angle of attack and as a result of a sudden contact between the fluid and the ribs and also a reduction in the coflowing length (length of the rib) cause a cut in heat transfer by the fluid in farther parts from the solid wall (tip of the rib).

Exhumed shear zones often contain folded and/or dynamically recrystallized structures such as veins and pseudotachylytes that record contemporaneous brittle and ductile deformation representing mixed bulk rheology. Here, we constrain the conditions that promote the transitions between ductile and brittle deformation by investigating quartz veins with shear offsets in the Saddlebag Lake shear zone in the central Sierra Nevada, California. Mesozoic metasedimentary rocks within the shear zone contain transposed bedding, strong cleavage, dextrally rotated porphyroclasts, and a steep mineral lineation, which together suggest an overall transpressive kinematic regime for the ductile deformation. Foliation sub-parallel veins are one subset of the veins in the shear zone. They have observed horizontal trace lengths of up to around 5 meters, though most are obscured by limited exposure, and displacements range from ~3-30 mm, with 1-5 mm of opening. Foliation sub-parallel veins are folded with the foliation and quartz microstructures and fluid inclusion thermobarometry measurements from vein samples indicate temperatures during vein formation by fracture were between 300-680°C. Quartz δ18O values (+5.9 to +16.5) suggest extended fluid-rock interaction that involved magmatic (δ18O ~ +8 to +10) and meteoric (δ18O down to -1) fluids. Foliation sub-parallel veins are most abundant in relatively massive, quartz-rich rocks where they are boudinaged, indicating they were rigid inclusions after formation. Based on the orientation and spatial distribution of the veins, we infer that they formed under high differential stress with pore pressures sufficiently high for the rocks to be critically stressed for shear failure along mechanically weak foliation planes. These observations suggest high pore pressures and mechanical heterogeneity at a variety of scales are necessary conditions for nucleation of shear fractures within ductile shear zones.

The presence of precipitated wax or even just low temperatures may induce non-Newtonian rheological behavior in crude oils. Such behavior can be found at operating conditions, for instance, in reservoirs at deep-water conditions. Therefore, reliable rheological models for crude oils applicable over the wide range of conditions the fluid may encounter are essential for a large number of oil technology applications. Such models must also be composition dependent, as many applications require predicting the rheological behavior of the fluid under strong compositional changes, e.g., recovery applications such as vapor extraction (VAPEX) processes or blending of fluids for improved rheological characteristics for piping, among many other applications. In this study, a comparative analysis between some published models applicable to the description of the non-Newtonian behavior of crude oils is carried out. Emphasis is placed on the stability of the model predictions within the wide range of conditions that may be encountered.

Full Text Available In this paper, we have considered the blood flow in a curved channel with abnormal development of stenosis in an axis-symmetric manner. The constitutive equations for incompressible and steady non-Newtonian tangent hyperbolic fluid have been modeled under the mild stenosis case. A perturbation technique and homotopy perturbation technique have been used to obtain analytical solutions for the wall shear stress, resistance impedance to flow, wall shear stress at the stenosis throat and velocity profile. The obtained results have been discussed for different tapered arteries i.e., diverging tapering, converging tapering, non-tapered arteries with the help of different parameters of interest and found that tapering dominant the curvature of the curved channel.

The challenge of this work is to connect physics with the concept of intelligence. By intelligence we understand a capability to move from disorder to order without external resources, i.e., in violation of the second law of thermodynamics. The objective is to find such a mathematical object described by ODE that possesses such a capability. The proposed approach is based upon modification of the Madelung version of the Schrodinger equation by replacing the force following from quantum potential with non-conservative forces that link to the concept of information. A mathematical formalism suggests that a hypothetical intelligent particle, besides the capability to move against the second law of thermodynamics, acquires such properties like self-image, self-awareness, self-supervision, etc. that are typical for Livings. However since this particle being a quantum-classical hybrid acquires non-Newtonian and non-quantum properties, it does not belong to the physics matter as we know it: the modern physics should be complemented with the concept of the information force that represents a bridge to intelligent particle. As a follow-up of the proposed concept, the following question is addressed: can artificial intelligence (AI) system composed only of physical components compete with a human? The answer is proven to be negative if the AI system is based only on simulations, and positive if digital devices are included. It has been demonstrated that there exists such a quantum neural net that performs simulations combined with digital punctuations. The universality of this quantum-classical hybrid is in capability to violate the second law of thermodynamics by moving from disorder to order without external resources. This advanced capability is illustrated by examples. In conclusion, a mathematical machinery of the perception that is the fundamental part of a cognition process as well as intelligence is introduced and discussed.

Polymer fluids are modeled with dissipative particle dynamics (DPD) as undiluted bead-spring chains and their solutions. The models are assessed by investigating their steady shear-rate properties. Non-Newtonian viscosity and normal stress coefficients, for shear rates from the lower to the upper Newtonian regimes, are calculated from both plane Couette and plane Poiseuille flows. The latter is realized as reverse Poiseuille flow (RPF) generated from two Poiseuille flows driven by uniform body forces in opposite directions along two-halves of a computational domain. Periodic boundary conditions ensure the RPF wall velocity to be zero without density fluctuations. In overlapping shear-rate regimes the RPF properties are confirmed to be in good agreement with those calculated from plane Couette flow with Lees-Edwards periodic boundary conditions (LECs), the standard virtual rheometer for steady shear-rate properties. The concentration and the temperature dependence of the properties of the model fluids are shown to satisfy the principles of concentration and temperature superposition commonly employed in the empirical correlation of real polymer-fluid properties. The thermodynamic validity of the equation of state is found to be a crucial factor for the achievement of time-temperature superposition. With these models, RPF is demonstrated to be an accurate and convenient virtual rheometer for the acquisition of steady shear-rate rheological properties. It complements, confirms, and extends the results obtained with the standard LEC configuration, and it can be used with the output from other particle-based methods, including molecular dynamics, Brownian dynamics, smooth particle hydrodynamics, and the lattice Boltzmann method.

Three-dimensional numerical calculations have been performed to simulate the viscous and porous inertia effects on the pressure drop in a non-Newtonianfluid flow through a porous medium. Cubes placed in an infinite space have been proposed as a three-dimensional model of microscopic porous structure. A full set of three-dimensional momentum equations is solved along with the continuity equation at a pore scale, so as to simulate a flow through an infinite number of obstacles arranged in a regular pattern. The microscopic numerical results, thus obtained, are processed to extract the macroscopic relationship between the pressure gradient-mass flow rate. Comparing the results based on the two- and three-dimensional models, it has been found that only the three-dimensional model can capture the porous inertia effects on the pressure drop correctly. 13 refs., 6 figs.

Non-Newtonian flow behavior was examined for butadiene-styrene (BS) diblock and BSB triblock copolymers dissolved in a S-selective solvent, dibutyl phthalate (DBP). Spherical domains of the non-solvated B blocks were arranged on a bcc lattice in both solutions at equilibrium, as revealed from SANS. The solutions exhibited significant thinning under steady flow, which was well correlated with the disruption of the bcc lattice detected with SANS. The lattice disruption was most prominent at a shear rate comparable to the frequency of B/S concentration fluctuation. For the BS/DBP solution, the recovery of the lattice structure after cessation of flow was the slowest for the most heavily disrupted lattice, as naturally expected. In contrast, for the BSB/DBP solution, the recovery rate was insensitive to the magnitude of lattice disruption. This peculiar behavior of the BSB solution suggests that the rate-determining step of the recovery in this solution is the transient B/S mixing required for reformation of the S bridges connecting the B domains.

Non-Newtonian rheological behaviour in crude oils can be induced by the presence of precipitated wax in reservoir fluids or by low ambient temperatures in heavy oils. This type of behaviour exists at low temperature operating conditions in deep-water production, or in the case of vapor extraction (VAPEX) processes of heavy oils involving strong compositional related changes to the already non-Newtonian viscosity of the oil. Reliable rheological models are needed for crude oils over the wide range of conditions that the fluid may encounter. The models should be of a compositional nature because the rheological behaviour of the fluid must be predicted in many applications, including VAPEX processes or fluid blending for piping. This study compared some published models that describe the non-Newtonian behaviour of crude oils. The emphasis was on the stability of the models predictions within the wide range of conditions that may be encountered. The study also evaluated the prediction potential of the analyzed models.

Measurements of the mean and turbulent flow characteristics of shear-thinning moderately elastic 0.1% and 0.2% xanthan gum aqueous solutions were carried out in a sudden expansion having a diameter ratio of 2. The inlet flow was turbulent and fully developed, and the results were compared with data for water in the same geometry and with previous published Newtonian and non-Newtonian data in a smaller expansion of diameter ratio equal to 1.538. An increase in expansion ratio led to an increase in the recirculation length and in the axial normal Reynolds stress at identical normalised locations, but the difference between Newtonian and non-Newtonian characteristics was less intense than in the smaller expansion. An extensive comparison of mean and turbulent flow characteristics was carried out in order to understand the variation of flow features. (orig.)

Bacteria often live in dynamic fluid environments and flow can affect fundamental microbial processes such as nutrient uptake and infection. However, little is known about the consequences of the forces and torques associated with fluid flow on bacteria. Through microfluidic experiments, we show that fluidshear produces strong spatial heterogeneity in suspensions of motile bacteria, characterized by up to 70% cell depletion from low-shear regions due to `trapping’ in high-shear regions. Two mathematical models and a scaling analysis accurately capture these observations, including the maximal depletion at mean shear rates of 2.5-10 s-1, and reveal that trapping by shear originates from the competition between the cell alignment with the flow and the stochasticity in the swimming orientation. We show that this shear-induced trapping directly impacts widespread bacterial behaviours, by hampering chemotaxis and promoting surface attachment. These results suggest that the hydrodynamic environment may directly affect bacterial fitness and should be carefully considered in the study of microbial processes.

Shear localization occurs in various instances of material instability in solid mechanics and is typically associated with Hadamard-instability for an underlying model. While Hadamard instability indicates the catastrophic growth of oscillations around a mean state, it does not by itself explain the formation of coherent structures typically observed in localization. The latter is a nonlinear effect and its analysis is the main objective of this article. We consider a model that captures the main mechanisms observed in high strain-rate deformation of metals, and describes shear motions of temperature dependent non-Newtonianfluids. For a special dependence of the viscosity on the temperature, we carry out a linearized stability analysis around a base state of uniform shearing solutions, and quantitatively assess the effects of the various mechanisms affecting the problem: thermal softening, momentum diffusion and thermal diffusion. Then, we turn to the nonlinear model, and construct localized states—in the form of similarity solutions—that emerge as coherent structures in the localization process. This justifies a scenario for localization that is proposed on the basis of asymptotic analysis in uc(Katsaounis) and uc(Tzavaras) (SIAM J Appl Math 69:1618-1643, 2009).

Shear localization occurs in various instances of material instability in solid mechanics and is typically associated with Hadamard-instability for an underlying model. While Hadamard instability indicates the catastrophic growth of oscillations around a mean state, it does not by itself explain the formation of coherent structures typically observed in localization. The latter is a nonlinear effect and its analysis is the main objective of this article. We consider a model that captures the main mechanisms observed in high strain-rate deformation of metals, and describes shear motions of temperature dependent non-Newtonianfluids. For a special dependence of the viscosity on the temperature, we carry out a linearized stability analysis around a base state of uniform shearing solutions, and quantitatively assess the effects of the various mechanisms affecting the problem: thermal softening, momentum diffusion and thermal diffusion. Then, we turn to the nonlinear model, and construct localized states - in the form of similarity solutions - that emerge as coherent structures in the localization process. This justifies a scenario for localization that is proposed on the basis of asymptotic analysis in \\\\cite{KT}.

In this paper, we study shearing spherically symmetric homogeneous density fluids in comoving coordinates. It is found that the expansion of the four-velocity of a perfect fluid is homogeneous, whereas its shear is generated by an arbitrary function of time M(t), related to the mass function of the distribution. This function is found to bear a functional relationship with density. The field equations are reduced to two coupled first order ordinary differential equations for the metric coefficients, g 11 and g 22. We have explored a class of solutions assuming that M is a linear function of the density. This class embodies, as a subcase, the complete class of shear-free solutions. We have discussed the off quoted work of Kustaanheimo (1947) and have noted that it deals with shear-free fluids having anisotropic pressure. It is shown that the anisotropy of the fluid is characterized by an arbitrary function of time. We have discussed some issues of historical priorities and credentials related to shear-free sol...

The paper discusses the flow of an incompressible non-Newtonianfluid due to stretching of a plane elastic surface in a saturated porous medium in the approximation of boundary layer theory. An exact analytical solution of non-linear MHD momentum equation governing the self-similar flow is given. The skin friction co-efficient decreases with an increase in the visco-elastic parameter k1 and increase in the values of both the magnetic parameter and permeability parameter.

Shear thinning—a reduction in suspension viscosity with increasing shear rates—is understood to arise in colloidal systems from a decrease in the relative contribution of entropic forces. The shear-thinning phenomenon has also been often reported in experiments with noncolloidal systems at high volume fractions. However its origin is an open theoretical question and the behavior is difficult to reproduce in numerical simulations where shear thickening is typically observed instead. In this letter we propose a non-Newtonian model of interparticle lubrication forces to explain shear thinning in noncolloidal suspensions. We show that hidden shear-thinning effects of the suspending medium, which occur at shear rates orders of magnitude larger than the range investigated experimentally, lead to significant shear thinning of the overall suspension at much smaller shear rates. At high particle volume fractions the local shear rates experienced by the fluid situated in the narrow gaps between particles are much larger than the averaged shear rate of the whole suspension. This allows the suspending medium to probe its high-shearnon-Newtonian regime and it means that the matrix fluid rheology must be considered over a wide range of shear rates.

This project concerned the development of a new fast finite element algorithm to solve flow problems of non-Newtonianfluids such as solutions or melts of polymers. Many constitutive theories for such materials involve single integrals over the deformation history of the particle at the stress evaluation point; examples are the Doi-Edwards and Curtiss-Bird molecular theories and the BKZ family derived from continuum arguments. These theories are believed to be among the most accurate in describing non-Newtonian effects important to polymer process design, effects such as stress relaxation, shear thinning, and normal stress effects. This research developed an optimized version of the algorithm which would run a factor of two faster than the pilot algorithm on scalar machines and would be able to take full advantage of vectorization on machines. Significant progress was made in code vectorization; code enhancement and streamlining; adaptive memory quadrature; model problems for the High Weissenberg Number Problem; exactly incompressible projection; development of multimesh extrapolation procedures; and solution of problems of physical interest. A portable version of the code is in the final stages of benchmarking and testing. It interfaces with the widely used FIDAP fluid dynamics package.

Active particles are self-driven units capable of converting stored or ambient free-energy into systematic movement. We discuss here the case when such particles move through non-Newtonianfluids. Neglecting inertial forces, we employ the reciprocal theorem to calculate the propulsion velocity of a single swimmer in a weakly non-Newtonianfluid with background flow. We also derive a general expression for the velocity of an active particle modelled as a squirmer in a second-order fluid. We then discuss how active colloids are affected by the medium rheology, namely viscoelasticity and shear-thinning.

The inks used in gravure-offset printing are non-Newtonianfluids with higher viscosities and lower surface tensions compared to Newtonian fluids. This paper examines the transfer of a non-Newtonian ink between two parallel plates when the top plate is moved upward with a constant velocity while the bottom plate is held fixed. Numerical simulations were carried out using the Carreau model to explore the behavior of a non-Newtonian ink in gravure-offset printing. The volume of fluid (VOF) model was adopted to demonstrate the stretching and break-up behaviors of the ink. The results indicate that the ink transfer ratio is greatly influenced by the contact angle, especially the contact angle at the upper plate ({alpha}). For lower values of {alpha}, oscillatory or unstable behavior of the position of minimum thickness of the ink between the two parallel plates during the stretching period is observed. This oscillation gradually diminishes as the contact angle at the upper plate is increased. Moreover, the number of satellite droplets increases as the velocity of the upper plate is increased. The surface tension of the conductive ink shows a positive impact on the ink transfer ratio to the upper plate. Indeed, the velocity of the upper plate has a significant influence on the ink transfer in gravure-offset printing when the Capillary number (Ca) is greater than 1 and the surface tension dominates over the ink transfer process when Ca is less than 1.

The thesis investigates the flow of non-Newtonianfluids in porous media using pore-scale network modeling. Non-Newtonianfluids show very complex time and strain dependent behavior and may have initial yield stress. Their common feature is that they do not obey the simple Newtonian relation of proportionality between stress and rate of deformation. They are generally classified into three main categories: time-independent, time-dependent and viscoelastic. Two three-dimensional networks representing a sand pack and Berea sandstone were used. An iterative numerical technique is used to solve the pressure field and obtain the flow rate and apparent viscosity. The time-independent category is investigated using two fluid models: Ellis and Herschel-Bulkley. The analysis confirmed the reliability of the non-Newtonian network model used in this study. Good results are obtained, especially for the Ellis model, when comparing the network model results to experimental data sets found in the literature. The yield-stres...

In this work, analytical predictions of the rectilinear flow of a non-Newtonian liquid are given. The fluid is subjected to a combined flow: A pulsatile time-dependent pressure gradient and a random longitudinal vibration at the wall acting simultaneously. The fluctuating component of the combined pressure gradient and oscillating flow is assumed to be of small amplitude and can be adequately represented by a weakly stochastic process, for which a quasi-static perturbation solution scheme is suggested, in terms of a small parameter. This flow is analyzed with the Tanner constitutive equation model with the viscosity function represented by the Ellis model. According to the coupled Tanner-Ellis model, the flow enhancement can be separated in two contributions (pulsatile and oscillating mechanisms) and the power requirement is always positive and can be interpreted as the sum of a pulsatile, oscillating, and the coupled systems respectively. Both expressions depend on the amplitude of the oscillations, the perturbation parameter, the exponent of the Ellis model (associated to the shear thinning or thickening mechanisms), and the Reynolds and Deborah numbers. At small wall stress values, the flow enhancement is dominated by the axial wall oscillations whereas at high wall stress values, the system is governed by the pulsating noise perturbation. The flow transition is obtained for a critical shear stress which is a function of the Reynolds number, dimensionless frequency and the ratio of the two amplitudes associated with the pulsating and oscillating perturbations. In addition, the flow enhancement is compared with analytical and numerical predictions of the Reiner-Phillipoff and Carreau models. Finally, the flow enhancement and power requirement are predicted using biological rheometric data of blood with low cholesterol content.

Recently, various non-invasive tools such as the magnetic resonance image (MRI), ultrasound imaging (USI), computed tomography (CT), and the computational fluid dynamics (CFD) have been widely utilized to enhance our current understanding of the physiological parameters that affect the initiation and the progression of the cardiovascular diseases (CVDs) associated with heart failure (HF). In particular, the hemodynamics of left ventricle (LV) has attracted the attention of the researchers due to its significant role in the heart functionality. In this study, CFD owing its capability of predicting detailed flow field was adopted to model the blood flow in images-based patient-specific LV over cardiac cycle. In most published studies, the blood is modeled as Newtonian that is not entirely accurate as the blood viscosity varies with the shear rate in non-linear manner. In this paper, we studied the effect of Newtonian assumption on the degree of accuracy of intraventricular hemodynamics. In doing so, various non-Newtonian models and Newtonian model are used in the analysis of the intraventricular flow and the viscosity of the blood. Initially, we used the cardiac MRI images to reconstruct the time-resolved geometry of the patient-specific LV. After the unstructured mesh generation, the simulations were conducted in the CFD commercial solver FLUENT to analyze the intraventricular hemodynamic parameters. The findings indicate that the Newtonian assumption cannot adequately simulate the flow dynamic within the LV over the cardiac cycle, which can be attributed to the pulsatile and recirculation nature of the flow and the low blood shear rate.

Non-Newtonianfluid model for blood flow through a tapered artery with a stenosis and variable viscosity by modeling blood as Jeffrey fluid has been studied in this paper. The Jeffrey fluid has two parameters, the relaxation time A1 and retardation time A2. The governing equations are simplified using the case of mild stenosis. Perturbation method is used to solve the resulting equations. The effects of non-Newtonian nature of blood on velocity profile, temperature profile, wall shear stress, shearing stress at the stenotsis throat and impedance of the artery are discussed. The results for Newtonian fluid are obtained as special case from this model.

Full Text Available Well test analysis for polymer flooding is different from traditional well test analysis because of the non-Newtonian properties of underground flow and other mechanisms involved in polymer flooding. Few of the present works have proposed a numerical approach of pressure transient analysis which fully considers the non-Newtonian effect of real polymer solution and interprets the polymer rheology from details of pressure transient response. In this study, a two-phase four-component fully implicit numerical model incorporating shear thinning effect for polymer flooding based on PEBI (Perpendicular Bisection grid is developed to study transient pressure responses in polymer flooding reservoirs. Parametric studies are conducted to quantify the effect of shear thinning and polymer concentration on the pressure transient response. Results show that shear thinning effect leads to obvious and characteristic nonsmoothness on pressure derivative curves, and the oscillation amplitude of the shear-thinning-induced nonsmoothness is related to the viscosity change decided by shear thinning effect and polymer concentration. Practical applications are carried out with shut-in data obtained in Daqing oil field, which validates our findings. The proposed method and the findings in this paper show significant importance for well test analysis for polymer flooding and the determination of the polymer in situ rheology.

An experimental description of the flow structure of non-Newtonian slurries in the laminar, transitional, and full turbulent pipe flow regimes is the primary objective of this research. Measurements include rheological characterization of the fluid and local fluid velocity measurements with a Laser Doppler Velocimeter (LDV). Optical access to the flow is gained through a test section and model slurry which are both transparent. The model slurry is formulated from silica gel particles and hydrocarbon liquid mixture whose indices of refraction are matched so that light is not scattered from the particles. Experiments are being conducted in a large-scale pipe slurry. Flow measurements including turbulence quantities such as Reynolds stress were measured with a two-component two-color LDV. The present research indicates that non-Newtonian slurries are possible with concentrations of a few percent by weight of small particles whose sizes are two microns or less. A non-Newtonian slurry from small particles could maintain large particles (one millimeter size) at high concentrations in suspension almost indefinitely. Such a slurry would prevent particle fallout and its associated problems.

Assuming that the Hagedorn fluid composed of known particles and resonances with masses m <2 GeV obeys the first-order theory (Eckart) of relativistic fluid, we discuss the transport properties of QCD confined phase. Based on the relativistic kinetic theory formulated under the relaxation time approximation, expressions for bulk and shear viscosity in thermal medium of hadron resonances are derived. The relaxation time in the Hagedorn dynamical fluid exclusively takes into account the decay and eventually van der Waals processes. We comment on the in-medium thermal effects on bulk and shear viscosity and averaged relaxation time with and without the excluded-volume approach. As an application of these results, we suggest the dynamics of heavy-ion collisions, non-equilibrium thermodynamics and the cosmological models, which require thermo- and hydro-dynamics equations of state. (Abstract Copyright [2010], Wiley Periodicals, Inc.)

Assuming that the Hagedorn fluid composed of known particles and resonances with masses $m<2\\,$GeV obeys the {\\it first-order} theory (Eckart) of relativistic fluid, we discuss the transport properties of QCD confined phase. Based on the relativistic kinetic theory formulated under the relaxation time approximation, expressions for bulk and shear viscosity in thermal medium are derived. The relaxation time in the Hagedorn dynamical fluid exclusively takes into account the decay and eventually van der Waals processes. We comment on the {\\it in-medium} thermal effects on bulk and shear viscosities and averaged relaxation time with and without the excluded-volume approach. As an application of these results, we suggest the dynamics of heavy-ion collisions, non-equlibrium thermodynamics and the cosmological models, which require thermo and hydrodynamics equations of state.

The swimming behaviour of microorganisms can be strongly influenced by the rheology of their fluid environment. In this manuscript, we experimentally investigate the effects of shear-thinning viscosity on the swimming behaviour of an undulatory swimmer, the nematode Caenorhabditis elegans. Tracking methods are used to measure the swimmer's kinematic data (including propulsion speed) and velocity fields. We find that shear-thinning viscosity modifies the velocity fields produced by the swimming nematode but does not modify the nematode's speed and beating kinematics. Velocimetry data show significant enhancement in local vorticity and circulation, and an increase in fluid velocity near the nematode's tail, compared to Newtonian fluids of similar effective viscosity. These findings are in good agreement with recent theoretical and numerical results.

Fluid migration in metamorphic environments depends on a dynamically evolving permeable pore space, which was rarely characterised in detail. The data-base behind our understanding of the 4-dimensional transport properties of metamorphic rocks is therefore fragmentary at best, which leaves conceptual models poorly supported. Generally, it seems established that deformation is a major driver of permeability generation during regional metamorphism, and evidence for metamorphic fluids being channelled in large scale shear zones has been found in all depth segments of the continental crust. When strain localizes in ductile shear zones, the microfabric is modified until a steady state mylonite is formed that supports large deformations. A dynamic porosity that evolves during mylonitisation controls the distinct transport pathways along which fluid interacts with the rock. This dynamic porosity is controlled by a limited number of mechanisms, which are intrinsically linked to the metamorphic evolution of the rock during its deformational overprint. Many mid- and lower-crustal mylonites comprise polyphase mixtures of micron-sized grains that show evidence for deformation by dissolution/precipitation-assisted viscous grain boundary sliding. The establishment of these mineral mixtures is a critical process, where monomineralic layers are dispersed and grain growth is inhibited by the heterogeneous nucleation of secondary mineral phases at triple junctions. Here we show evidence from three different mid- and lower-crustal shear zones indicating that heterogeneous nucleation occurs in creep cavities. Micro- and nanotomographic observations show that creep cavities provide the dominant form of porosity in these ultramylonites. They control a "granular fluid pump" that directs fluid migration and hence mass transport. The granular fluid pump operates on the grain scale driven by viscous grain boundary sliding, and requires only small amounts of fluid. The spatial arrangement of

为准确、有效地模拟非等温非牛顿黏性流体的流动问题，本文基于一种不含核导数计算的核梯度修正格式和不可压缩条件给出了一种改进光滑粒子动力学(SPH)离散格式，它较传统SPH离散格式具有较高精度和较好稳定性。同时，为准确地描述温度场的演化过程，建立了非牛顿黏性的SPH温度离散模型。通过对等温Poiseuille流、喷射流和非等温Couette流、4：1收缩流进行模拟，并与其他数值结果作对比，分别验证了改进SPH方法模拟非牛顿黏性流动问题的可靠性和提出的SPH温度离散模型求解非等温流动问题的有效性和准确性。随后，运用改进SPH方法结合SPH温度离散模型对环形腔和C形腔内非等温非牛顿黏性流体的充模过程进行了试探性模拟研究，分析了数值模拟的收敛性，讨论了不同位置处热流参数对温度和流动的影响。%In this paper, a corrected smoothed particle hydrodynamics (SPH) method is proposed to solve the problems of non-isothermal non-Newtonian viscous fluid. The proposed particle method is based on the corrected kernel derivative scheme under no kernel derivative and incompressible conditions, which possesses higher accuracy and better stability than the traditional SPH method. Meanwhile, a temperature-discretization scheme is deduced by the concept of SPH method for the purpose of precisely describing the evolutionary process of the temperature field. Reliability of the corrected SPH method for simulating the non-Newtonian viscous fluid flow is demonstrated by simulating the isothermal Poiseuille flow and the jet fluid of filling process; and the validity and accuracy of the proposed SPH discrete scheme in a temperature model for solving the non-isothermal fluid flow are tested by solving the non-isothermal Couette flow and 4:1 contraction flow. Subsequently, the proposed corrected SPH method combined with the SPH temperature

We solve exactly the Poiseuille and Couette flows of a non-Newtonianfluid discussed by Roohi et al (2009 Phys. Scr. 79 065009) and thereby show that the approximate analytical solutions provided by the homotopy method must be used with caution.

Non-Newtonianfluid flow in porous media is of considerable interest in hydrology, chemical and petroleum engineering, and biofluid mechanics. We consider an infinite porous domain of plane (d=1), cylindrical (d=2) or semi-spherical geometry (d=3), having uniform permeability k and porosity Φ, initially at uniform pressure and saturated by a weakly compressible non-Newtonianfluid, and analyze the dynamics of the pressure variation generated within the domain by an instantaneous mass injection m0 in its origin. The fluid is described by a rheological power-law model of given consistency index H and flow behavior index n; the flow law is a modified Darcy's law depending on H, Φ, n. Coupling flow law and mass balance equations yields the nonlinear partial differential equation governing the pressure field; an analytical solution is derived in space r and time t as a function of a self-similar variable η=r/tβ(n). We revisit and expand the work in previous papers by providing a dimensionless general formulation and solution to the problem for d=1,2,3. When a shear-thinning fluid (nfluids; the front velocity is proportional to t(n-2)/2 in plane geometry, t(2n-3)/(3-n) in cylindrical geometry, and t(3n-4)/(4-2n) in semi-spherical geometry. The front position is a markedly increasing function of n and is inversely dependent on d; the pressure front advances at a slower rate for larger values of compressibility, higher injected mass and lower porosity. When pressure is considered, it is seen that an increase in d from 1 to 3 brings about an order of magnitude reduction. An increase in compressibility implies a significant decrease in pressure, especially at early times. To reflect the uncertainty inherent in values of the problem parameters, we then consider selected properties of fluid (flow behavior index n) and porous domain (permeability k, porosity Φ, and medium compressibility cp) as independent random variables with uniform probability distribution. The

In this study, a strategy for designing optimal shim configuration inside a slot die is suggested to assure the uniform coating flow distribution of various non-Newtonianshear-thinning liquids at the die exit in a slot coating system. Flow patterns of non-Newtonian liquids inside the slot die, via three-dimensional computations, have been compared using various shim geometries which can adjust the flow region in a slot manifold. The rather non-uniform (parabolic) velocity distributions of shear-thinning liquids at the die exit under the basic shim condition could be effectively flattened by the modification of shim geometry without the change of die manifold structure. Dimensions of hybrid shims for controlling flow features at edge and center regions within slit channel are positively tuned, according to the shear-thinning level of coating liquids.

Effects of non-Newtonian viscosity for surfactant solution on the vortex characteristics and drag-reducing rate in a swirling pipe flow are investigated by pressure drop measurements, velocity profile measurements and viscosity measurements. Non-Newtonian viscosity is represented by power-law model (τ = kD n). Surfactant solution used has shear-thinning viscosity with n ＜ 1.0. The swirling flow in this study has decay of swirl and vortex-type change from Rankin's combined vortex to forced vortex. It is shown that the effect of shear-thinning viscosity on the decay of swirl intensity is different by vortex category and the critical swirl number with the vortex-type change depends on shear-thinning viscosity.

Full Text Available This research deals with experimental work on solid suspension and dispersion in stirred tank reactors that operate with complex fluids. Only suspended speed (Njs throughout the vessel was characterized using Gamma-Ray Densitometry. The outcomes of this study help to understand solid suspension mechanisms involving changes the rheology of the fluid and provide engineering data for designing stirred tanks. All experiments were based on classic radial and axial flow impellers, i.e., Rushton Turbine (RT and Pitched Blade Turbine in down pumping mode (PBT-D. Three different liquids (water, water+CMC, and water+PAA were employed in several concentrations. The CMC solution introduced as a pseudo plastic fluid and PAA solution was applied as a Herschel Bulkley fluid. The rheological properties of these fluids were characterized separately. According to the findings, the critical impeller speeds for solid suspension for non-Newtonianfluids were more eminent than those for water. Experiments were performed to characterize the effects of solid loading, impeller clearance and viscosity on Njs. Also the PSO method is employed to find suitable parameters of Zwietering's correlation for prediction of Njs in NonNewtonianfluids.

The steady state of a dilute gas enclosed between two infinite parallel plates in relative motion and under the action of a uniform body force parallel to the plates is considered. The Bhatnagar-Gross-Krook model kinetic equation is analytically solved for this Couette-Poiseuille flow to first order in the force and for arbitrary values of the Knudsen number associated with the shear rate. This allows us to investigate the influence of the external force on the non-Newtonian properties of the...

A Lagrangian method for the simulation of flow of non-Newtonian liquids is implemented. The fluid mechanical equations are formulated in the form of a variational principle, and a discretization is performed by finite elements. The method is applied to the slow of a contravariant convected Maxwell...... liquid around a sphere moving axially in a cylinder. The simulations show that the friction factor for a sphere in a narrow cylinder is a rapidly decreasing function of the Deborah number, while the friction factor for a sphere in a very wide cylinder is not significantly affected by fluid elasticity...

Peristaltic motion of a non-Newtonian Carreau fluid is analyzed in a curved channel under the long wavelength and low Reynolds number assumptions, as a simulation of digestive transport. The flow regime is shown to be governed by a dimensionless fourth-order, nonlinear, ordinary differential equation subject to no-slip wall boundary conditions. A well-tested finite difference method based on an iterative scheme is employed for the solution of the boundary value problem. The important phenomena of pumping and trapping associated with the peristaltic motion are investigated for various values of rheological parameters of Carreau fluid and curvature of the channel. An increase in Weissenberg number is found to generate a small eddy in the vicinity of the lower wall of the channel, which is enhanced with further increase in Weissenberg number. For shear-thinning bio-fluids (power-law rheological index, n Weissenberg number displaces the maximum velocity toward the upper wall. For shear-thickening bio-fluids, the velocity amplitude is enhanced markedly with increasing Weissenberg number.

Experimental data on the pressure drop across different types of elbow for non-Newtonian pseudoplastic liquid flow in laminar condition have been presented. A generalized correlation has been developed for predicting the frictional pressure drop across the elbows in the horizontal plane.

This paper deals with fast and reliable numerical solution methods for the incompressible non-Newtonian Navier-Stokes equations. To handle the nonlinearity of the governing equations, the Picard and Newton methods are used to linearize these coupled partial differential equations. For space discreti

The dominant driving force for plate tectonics is slab pull, in which sinking slabs pull the trailing plate. Forward plate velocities are typically similar in magnitude (7 cm/yr) as estimates for sinking velocities of slabs through the upper mantle. However, these estimates are based on data for slabs that are coherent into the transition zone as well as models that considered the upper mantle to be entirely Newtonian. Dislocation creep in the upper mantle can strongly influence mantle flow, and is likely activated for flow around vertically sinking slabs in the uppermost mantle. Thus, it is possible that in some scenarios, a non-Newtonian mantle will have an influence on plate motions but it is unclear to what degree. To address this question, we investigate how the non-Newtonian rheology modifies the sinking velocities of slablets (spherical, negatively buoyant and highly viscous blobs). The model set-up is similar to a Stokes sphere sinking, but is in 2-D cartesian with temperature-and stress-dependent rheology. For these numerical models, we use the Stag-YY code (e.g., Tackley 2008) and apply a pseudo-free surface using the 'sticky-air' approach (Matsumoto and Tomoda 1983; Schmeling et al, 2008, Crameri et al., 2012). The sinking blob is both highly viscous and compositionally dense, but is the same temperature as the background fluid which eliminates thermal diffusion and associated variations in thermal buoyancy. The model domain is 2x1 or 4x1 and allows enough distance to the sidewalls so that sinking velocities are not influenced by the boundary conditions. We compare our results with those previously obtained for salt diapirs rising through a power-law rheology mantle/crust (Weinberg, 1993; Weinberg and Podladchikov, 1994), which provided both numerical and analytic results. Previous results indicate a speed-up of an order of magnitude is possible. Finally, we then extend the models and analysis to mantle convection systems that include for single

In this video, Ray-tracing data visualization technique was used to obtain realistic and detailed flow motions during droplet collision. The differences of collision outcome between Newtonian and non-Newtonian were compared. Various types of droplet collision were presented, including bouncing, coalescence, and stretching separation. Because of the reducing of equivalent viscosity caused by shear stress, the gas film between shear-thinning droplet is thinner than Newtonian liquid. Since thinner gas film promotes coalescence, shear thinning liquid has smaller area of bouncing regime in the diagram of Weber number and impact parameter. During the ligament/thread breakup process of stretching separation, two kinds of instabilities are identified, helical and buckling instabilities. Helical instability is analogous to a viscous rotating liquid jet, while the buckling instability is analogous to electrically charged liquid jets of polymer solutions.

This article studies the Carreau viscosity model (which is a generalized Newtonian model) and then use it to obtain a formulation for the boundary layer equations of the Carreau fluid. The boundary layer flow and heat transfer to a Carreau model over a nonlinear stretching surface is discussed. The Carreau model, adequate for many non-Newtonianfluids, is used to characterize the behavior of the fluids having shear thinning properties and fluids with shear thickening properties for numerical ...

The particle and momentum balance equations can be solved on concentric circular flux surfaces to determine the effective viscous drag present in a magnetized tokamak plasma in the low aspect ratio limit. An analysis is developed utilizing the first-order Fourier expansion of the poloidal variation of quantities on the flux surface akin to that by Stacey and Sigmar [Phys. Fluids, 28, 9 (1985)]. Expressions to determine the poloidal variations of density, poloidal velocity, toroidal velocity, radial electric field, poloidal electric field, and other radial profiles are presented in a multi-species setting. Using as input experimental data for the flux surface averaged profiles of density, temperature, toroidal current, toroidal momentum injection, and the poloidal and toroidal rotations of at least one species of ion, one may solve the equations numerically for the remaining profiles. The resultant effective viscosities are compared to those predicted by Stacey and Sigmar and Shaing, et al., [Nuclear Fusion, 2...

The ability to absorb a large amount of energy during an impact event without generating critical damages represents a key feature of new generation composite systems. Indeed, the intrinsic layered nature of composite materials allows the embodiment of specific hybrid plies within the stacking sequence that can be exploited to increase impact resistance and damping of the entire structure without dramatic weight increase. This work is based on the development of an impact-resistant hybrid composite obtained by including a thin layer of Non-Newtonian silica based fluid in a carbon fibres reinforced polymer (CFRP) laminate. This hybrid phase is able to respond to an external solicitation by activating an order-disorder transition that thickens the fluid increasing its viscosity, hence dissipating the energy impact without any critical failure. Several Shear Thickening Fluids (STFs) were manufactured by changing the dimensions of the particles that constitute the disperse phase and their concentrations into the continuous phase. The dynamic viscosity of the different STFs was evaluated via rheometric tests, observing both shear thinning and shear thickening effects depending on the concentration of silica particles. The solutions were then embedded as an active layer within the stacking sequence to manufacture the hybrid CFRP laminates with different embedded STFs. Free vibration tests were carried out in order to assess the damping properties of the different laminates, while low velocity impact tests were used to evaluate their impact properties. Results indicate that the presence of the non-Newtonianfluid is able to absorb up to 45 % of the energy during an impact event for impacts at 2.5 m/s depending on the different concentrations and particles dimensions. These results were confirmed via C-Scan analyses to assess the extent of the internal delamination.

We consider weak solutions for a diffuse interface model of two non-Newtonian viscous, incompressible fluids of power-law type in the case of different densities in a bounded, sufficiently smooth domain. This leads to a coupled system of a nonhomogenouos generalized Navier-Stokes system and a Cahn-Hilliard equation. For the Cahn-Hilliard part a smooth free energy density and a constant, positive mobility is assumed. Using the {{L}∞} -truncation method we prove existence of weak solutions for a power-law exponent p>\\frac{2d+2}{d+2} , d = 2, 3.

Computational Fluid Dynamics (CFD) analysis have been carried out to evaluate the frictional pressure drop across the horizontal pipeline and different piping components, like elbows, orifices, gate and globe valves for non-Newtonian liquid through 0.0127 m pipe line. The mesh generation is done using GAMBIT 6.3 and FLUENT 6.3 is used for CFD analysis. The CFD results are verified with our earlier published experimental data. The CFD results show the very good agreement with the experimental values.

In this work, we study active particles with prescribed surface velocities in non-Newtonianfluids. We employ the reciprocal theorem to derive a general form of the propulsion velocity of a single active particle (or swimmer) in a weakly non-Newtonian background flow in the absence of inertia. Using this formulation, we obtain the velocity of an active spherical particle with an arbitrary axisymmetric slip-velocity in an otherwise quiescent second-order fluid. Finally, we determine how the motion of a diffusiophoretic Janus particle is affected by complex fluid rheology, namely viscoelasticity and shear-thinning. We find that a Janus particle may go faster or slower in a viscoelastic fluid, but is always slower in a shear-thinning fluid as compared to a Newtonian fluid.

Multi-fluid flows are frequently thought of as being less stable than single phase flows. Consideration of different non-Newtonian models can give rise to different types of hydrodynamic instability. Here we show that with careful choice of fluid rheologies and flow paradigm, one can achieve multi-l

Multi-fluid flows are frequently thought of as being less stable than single phase flows. Consideration of different non-Newtonian models can give rise to different types of hydrodynamic instability. Here we show that with careful choice of fluid rheologies and flow paradigm, one can achieve multi-l

In this investigation, the behavior of non-Newtonian nanofluid hydrodynamic and heat transfer are simulated. In this study, we numerically simulated a laminar forced non-Newtonian nanofluid flow containing a 0.5 wt% carboxy methyl cellulose (CMC) solutionin water as the base fluid with alumina at volume fractions of 0.5 and 1.5 as the solid nanoparticle. Numerical solution was modelled in Cartesian coordinate system in a two-dimensional microchannel in Reynolds number range of 10≤Re≤1000. The analyzed geometrical space here was a rectangular part of whose upper and bottom walls was influenced by a constant temperature. The effect of volume fraction of the nanoparticles, Reynolds number and non-Newtonian nanofluids was studied. In this research, the changes pressure drop, the Nusselt number, dimensionless temperature and heat transfer coefficient, caused by the motion of non-Newtonian nanofluids are described. The results indicated that the increase of the volume fraction of the solid nanoparticles and a reduction in the diameter of the nanoparticles would improve heat transfer which is more significant in Reynolds number. The results of the introduced parameters in the form of graphs drawing and for different parameters are compared.

In recent years the methods of computational fluid dynamics (CFD) have been applied to the human cardiovascular system to better understand the relationship between arterial blood flow and the disease process, for example in an abdominal aortic aneurysm (AAA). Obviously, the technical challenges associated with such modeling are formidable. Among the many problems to be addressed, in this paper we add yet another complication -- the known non-Newtonian nature of blood. In this preliminary study, we used a patient-based AAA model with rigid walls. The pulsatile nature of the flow and the RCR outflow boundary condition are considered. We use the Carreau-Yasuda model to describe the non-Newtonian viscosity variation. Preliminary results for 200K, 2M, and 8M elements mesh are presented for the Newtonian and non-Newtonian cases. The broad fundamental issue we wish to eventually resolve is whether or not non-Newtonian effects in blood flow are sufficiently strong in unhealthy vessels that they must be addressed in meaningful simulations. Interesting differences during the flow cycle shed light on the problem, but further research is needed.

In this work the possibility of detecting a non--Newtonian contribution to the gravitational potential by means of its effects upon the first and second--order coherence properties of light is analyzed. It will be proved that, in principle, the effects of a fifth force upon the correlation functions of electromagnetic radiation could be used to detect the existence of new forces. Some constraints upon the experimental parameters will also be deduced.

Propulsion through fluids is a key component in the life cycle of many microbes, be it in development, infection, or simply finding nutrients. In systems of biomedical relevance, this propulsion is often through polymer suspensions that endow the fluid with complex non-Newtonian properties, such as shear-thinning and viscoelastic behavior. Due to the complexity of three-dimensional (3D) non-Newtonian modeling, two-dimensional (2D) undulatory propulsion has recently been extensively studied as a means of garnering physical intuition for these systems. However, while streamlines, swimming speeds, and swimmer trajectories are strikingly similar in 2D and 3D Newtonian calculations, behavior in non-Newtonianfluids depends upon flow derivatives, such as the shear rate, which are radically different. Taking shear thinning as an example rheology, prevalent in biological fluids such as physiological mucus, this Rapid Communication demonstrates how failing to account for this difference can misguide our understanding of 3D non-Newtonian swimming.

Carotid siphon is known as one of the risky sites among the human intracranial arteries, which is prone to formation of atherosclerotic lesions. Indeed, scientists believe that accumulation of low density lipoprotein (LDL) inside the lumen is the major cause of atherosclerosis. To this aim, three types of internal carotid artery (ICA) siphon have been constructed to examine variations of hemodynamic parameters in different regions of the arteries. Providing real physiological conditions, blood considered as non-Newtonianfluid and real velocity and pressure waveforms have been employed as flow boundary conditions. Moreover, to have a better estimation of risky sites, the accumulation of LDL particles has been considered, which has been usually ignored in previous relevant studies. Governing equations have been discretized and solved via open source OpenFOAM software. A new solver has been built to meet essential parameters related to the flow and mass transfer phenomena. In contrast to the common belief regarding negligible effect of blood non-Newtonian behavior inside large arteries, current study suggests that the non-Newtonian blood behavior is notable, especially on the velocity field of the U-type model. In addition, it is concluded that neglecting non-Newtonian effects underestimates the LDL accumulation up to 3% in the U-type model at the inner side of both its bends. However, in the V and C type models, non-Newtonian effects become relatively small. Results also emphasize that the outer part of the second bend at the downstream is also at risk similar to the inner part of the carotid bends. Furthermore, from findings it can be implied that the risky sites strongly depend on the ICA shape since the extension of the risky sites are relatively larger for the V-type model, while the LDL concentrations are higher for the C-type model.

We present high-resolution 3D microstructures of three-phase magmas composed of melt, bubbles and crystals in different proportions deformed at magmatic pressure and temperature conditions. This study aims to constrain the dependence of rheological and physical properties of magmas on the viscosity of the silicate melt, the applied deformation rate, the relative contents of crystals and bubbles and on the interactions between these phases. The starting material is composed of a hydrous haplogranitic melt containing H2O (2.26 wt%) and CO2 (624 ppm) and different proportions of quartz crystals (between 24 and 65 vol%; 63-125 μm in diameter) and bubbles (between 9 and 12 vol%; 5-150 μm in diameter). Experiments were performed in simple shear using a HT-HP internally-heated Paterson-type rock deformation apparatus (Paterson and Olgaard, 2000) at strain rates ranging between 5×10-5 s-1 and 4×10-3 s-1, at a constant pressure of 200 MPa and temperatures ranging between 723 and 1023 K. Synchrotron based X-ray tomographic microscopy performed at the TOMCAT beamline (Stampanoni et al., 2006) at the Swiss Light Source enabled quantitative evaluation of the 3D microstructure. At high temperature and low strain rate conditions the silicate melt behaves as a Newtonian liquid (Webb and Dingwell, 1990). Higher deformation rates and the contemporary presence of gas bubbles and solid crystals make magma rheology more complex and non-Newtonian behaviour occurs. In all experimental runs two different non-Newtonian effects were observed: shear thinning (decrease of viscosity with increasing strain rate) in high crystal-content magmas (55-65 vol% crystals; 9-10 vol% bubbles) and shear thickening (increase of viscosity with increasing strain rate) in magmas at lower degree of crystallinity (24 vol% crystals; 12 vol% bubbles). Both behaviours were observed at intermediate crystal-content (44 vol% crystals; 12 vol% bubbles), with an initial thickening that subsequently gives way to

Full Text Available Aerospace propulsion often involves the spray and combustion of liquids. When a liquid is sprayed, large drops form first, in a process known as primary atomization. Then, each drop breaks up into smaller droplets, in a process known as secondary atomization. This determines final drop sizes, which affect the liquid’s evaporation and mixing rates and ultimately influence combustor efficiency. Little has been published concerning the secondary atomization of visco-elastic non-Newtonian liquids, such as gels. These substances have special potential as aerospace propellants, because they are safer to handle than their Newtonian liquid counterparts, such as water. Additionally, they can be injected at varying rates, allowing for more control than solid propellants. To learn more about the atomization process of these liquids, a liquid drop generator and a high-speed camera were used to create and measure the conditions at which different breakup modes occurred, as well as the time required for the process. These results were compared to experimental and theoretical results for Newtonian liquids. Based on the data, one can conclude that solutions that are more elastic require higher shear forces to break up. In addition, while Newtonian liquids form droplets as they atomize, visco-elastic non-Newtonian solutions form ligaments. As a result, a combustion system utilizing these types of propellants must be capable of generating these forces. It may also be necessary to find a way to transform the ligaments into more spherically-shaped droplets to increase combustion efficiency.

The flow of high-viscosity liquids inside micrometer-size holes can be substantially different from the flow in the bulk, non-confined state of the same liquid. Such non-Newtonian behavior can be employed to generate structural anisotropy in the frozen-in liquid, i.e., in the glassy state. Here, we report on the observation of non-Newtonian flow of an ultralow melting chalcogenide glass inside a silica microcapillary, leading to a strong deviation of the shear viscosity from its value in the bulk material. In particular, we experimentally show that the viscosity is radius-dependent, which is a clear indication that the microscopic rearrangement of the glass network needs to be considered if the lateral confinement falls below a certain limit. The experiments have been conducted using pressure-assisted melt filling, which provides access to the rheological properties of high-viscosity melt flow under previously inaccessible experimental conditions. The resulting flow-induced structural anisotropy can pave the way towards integration of anisotropic glasses inside hybrid photonic waveguides.

In the study of long time asymptotic behaviors of the solutions to a class system of the incompressible non-Newtonianfluid flows in R3, it is proved that the weak solutions decay in L2 norm at (1+t) and the error of difference between non-Newtonianfluid and linear equation is also investigated. The findings are mainly based on the classic Fourier splitting methods.

Do increasing doses of electromagnetic fields (EMFs) increase the hazards effect on blood? Studies on the blood of rats provide guidance for the assessment of occupational and public health significance of exposure to EMFs. Here, apparent additive viscosity of animal blood after exposing to EMFs (3,5 and 10 gauss) is examined. The results indicate that hematocrite (HCT) increased as EMF increases while the viscocity decreased with the increase of EMF. Red blood cell permeability, deformabilit...

While elastic solids support compressional and shear waves, waves in ideal compressible fluids are usually thought of as compressional waves. Here, a class of acoustic-gravity waves is studied in which the dilatation is identically zero, and the pressure and density remain constant in each fluid particle. These shear waves are described by an exact analytic solution of linearized hydrodynamics equations in inhomogeneous, quiescent, inviscid, compressible fluids with piecewise continuous parameters in a uniform gravity field. It is demonstrated that the shear acoustic-gravity waves also can be supported by moving fluids as well as quiescent, viscous fluids with and without thermal conductivity. Excitation of a shear-wave normal mode by a point source and the normal mode distortion in realistic environmental models are considered. The shear acoustic-gravity waves are likely to play a significant role in coupling wave processes in the ocean and atmosphere.

The double-entry bookkeeping promoted by Luca Pacioli in the fifteenth century could be considered a strong argument in behalf of the multiplicative calculus which can be developed from the Grossman and Katz non-newtonian calculus concept. In order to emphasize this statement we present a brief history of the accountancy in its early time and we make the point of Ellerman's research concerning the double-entry bookkeeping.; La comptabilité en partie double présentée par Luca Pacioli au quinzi...

We report an experimental test of non-Newtonian gravitational forces at mi- crometer range. To experimentally subtract off the Casimir force and the electrostatic force background, differential force measurements were performed by sensing the lateral force between a gold sphere and a density modulated source mass using a soft cantilever. The current sensitivity is limited by the patch electrostatic force, which is further improved by two dimensional (2D) force mapping. The preliminary result sets a model independent constraint on the Yukawa type force at this range.

The possible "phase diagrams'' for shear-induced phase transitions between two phases are collected. We consider shear-thickening and shear-thinning fluids, under conditions of both common strain rate and common stress in the two phases, and present the four fundamental shear stress vs. strain rate curves and discuss their concentration dependence. We outline how to construct more complicated phase diagrams, discuss in which class various experimental systems fall, and sketch how to reconstru...

The visco-elastic properties of liquids have been investigated using acoustical resonance method. Piezoquatrz performed tangential oscillations on the main resonance frequency of 74 kHz contacts by the one end of horizontal surface with the studied liquid layer covered by quartz cover-plate. So the stagnant shear waves are installed in layer. The solution of interaction of piezoquartz-liquid layer-cover-plate gives three methods of determination of the real shear modulus (G) and the tangent of mechanical loss angle (tan theta) of liquid. The first method is realized at smaller thickness of liquid layer then the length of shear wave. Liquids of different classes have been studied using this method: polymer liquids, oils, glycols and alcohols. The second method is connected with the propagation of shear wave in liquid layer, parameters of which are determined the G and tan theta. And the third method is based on the determination of limit shift of resonance frequencies at completes damping of shear wave in thick layer of liquid. All these three methods give satisfactory agreement of results.

Methods of Computational Fluid Dynamics are applied to simulate pulsatile blood flow in human vessels and in the aortic arch. The non-Newtonian behaviour of the human blood is investigated in simple vessels of actual size. A detailed time-dependent mathematical convergence test has been carried out. The realistic pulsatile flow is used in all simulations. Results of computer simulations of the blood flow in vessels of two different geometries are presented. For pressure, strain rate and velocity component distributions we found significant disagreements between our results obtained with realistic non-Newtonian treatment of human blood and widely used method in literature: a simple Newtonian approximation. A significant increase of the strain rate and, as a result, wall sear stress distribution, is found in the region of the aortic arch. We consider this result as theoretical evidence that supports existing clinical observations and those models not using non-Newtonian treatment underestimate the risk of disru...

An improved technique has been developed for studies of the shear viscosity of fluids. It utilizes an acoustic resonator as a four-terminal electrical device; the resonator's amplitude response may be determined directly and simply related to the fluid's viscosity. The use of this technique is discussed briefly and data obtained in several fluids is presented.

Full Text Available Entropy generation in adiabatic flow of highly concentrated non-Newtonian emulsions in smooth tubes of five different diameters (7.15–26.54 mm was investigated experimentally. The emulsions were of oil-in-water type with dispersed-phase concentration (Φ ranging from 59.61–72.21% vol. The emulsions exhibited shear-thinning behavior in that the viscosity decreased with the increase in shear rate. The shear-stress (τ versus shear rate (˙γ data of emulsions could be described well by the power-law model: τ=K˙γn. The flow behavior index n was less than 1 and it decreased sharply with the increase in Φ whereas the consistency index K increased rapidly with the increase in Φ . For a given emulsion and tube diameter, the entropy generation rate per unit tube length increased linearly with the increase in the generalized Reynolds number ( Re_n on a log-log scale. For emulsions with Φ ≤65.15 % vol., the entropy generation rate decreased with the increase in tube diameter. A reverse trend in diameter-dependence was observed for the emulsion with Φ of 72.21% vol. New models are developed for the prediction of entropy generation rate in flow of power-law emulsions in smooth tubes. The experimental data shows good agreement with the proposed models.

Full Text Available The influence of droplet size on exergy destruction rate in flow of highly concentrated oil-in-water emulsions was investigated experimentally in a cone and plate geometry. The oil concentration was fixed at 74.5% by volume. At this dispersed-phase (oil concentration, two different droplet size emulsions were prepared: fine and coarse emulsions. The fine and coarse emulsions were mixed in different proportions to vary the droplet size distribution. Although the dispersed and matrix phases of the emulsions were Newtonian in nature, the emulsions exhibited a non-Newtonian (shear-thinning behavior due to the high droplet concentration. The shear stress—shear rate data of the emulsions could be described adequately by a power law model. At low shear rates, the exergy destruction rate per unit volume of emulsion exhibited a minimum at a fine emulsion proportion of 35%. The results from the cone and plate geometry were used to simulate exergy loss in pipeline flow of emulsions. The pumping of emulsions becomes more efficient thermodynamically upon mixing of fine and coarse emulsions provided that the flow regime is maintained to be laminar and that the Reynolds number is kept at a low to moderate value. In the turbulent regime, the exergy loss generally increases upon mixing the fine and coarse emulsions.

Full Text Available The paper presents the rheological behavior study of some cationic surfactant-based aqueous solutions that can be used as fracturing fluids. It was followed the influence of salt type and concentration, as well as that of temperature by setting the dependence between the shear stress τ and the shear rate   . The analysis of dependence between τ and   demonstrates that all the studied solutions have non-Newtonian behavior with flow behavior index smaller than 1.

Full Text Available Continuity and momentum equations applied to the entrance region of an axial, incompressible, isothermal, laminar and steady flow of a power-law fluid in a concentric annulus, were solved by a finite difference implicit method. The Newtonian case was solved used for validation of the method and then compared to reported results. For the non-Newtonian case a pseudoplastic power-law model was assumed and the equations were transformed to obtain a pseudo-Newtonian system which enabled its solution using the same technique as that used for the Newtonian case. Comparison of the results for entrance length and pressure drop with those available in the literature showed a qualitative similarity, but significant quantitative differences. This can be attributed to the differences in entrance geometries and the definition of asymptotic entrance length.

Three processing methods were compared to develop a low dose (0.1%) immediate release tablet. Similar formulations were used to evaluate low shear, high shear, and fluid bed granulation methods. For each granulation process, the drug was dissolved or suspended in the granulating fluid and sprayed into the granulator. Both water and methanol were evaluated as granulating fluids. The low shear granulation was performed in a Patterson-Kelley V-Blender with I-bar. The high shear granulation was performed in a GRAL (top entry impeller) and a Diosna (bottom mounted impeller). Fluid bed granulation was also performed using top-spray. Acceptable content uniformity was obtained using each technology. The type of granulator and granulating solvent affected the granulation particle size distributions and bulk/tap densities. However, the addition of extragranular microcrystalline cellulose minimized the effect of variable granulation properties and allowed similar tablets to be produced from each granulation process.

We study the fluid-structure interaction dynamics of non-Newtonian flow through a slender linearly elastic cylinder at the creeping flow regime. Specifically, considering power-law fluids and applying the thin shell approximation for the elastic cylinder, we obtain a non-homogeneous p-Laplacian equation governing the viscous-elastic dynamics. We obtain exact solutions for the pressure and deformation fields for various initial and boundary conditions, for both shear thinning and shear thickening fluids. In particular, impulse or a step in inlet pressure yield self-similar solutions, which exhibit a compactly supported propagation front solely for shear thinning fluids. Applying asymptotic expansions, we provide approximations for weakly non-Newtonian behavior showing good agreement with the exact solutions sufficiently far from the front.

@@ Shear tests of an electrorheological fluid with pre-applied electric field and compression along the field direction are carried out. The results show that pre-compressions can increase the shear yield stress up to ten times. Under the same external electric field strength, a higher compressive strain corresponds to a larger shear yield stress enhancement but with slight current density decrease, which shows that the particle interaction potentials are not increased by compressions but the compression-induced chain aggregation dominates the shear yield stress improvement. This pre-compression technique might be useful [or developing high performance flexible ER or magnetorheological couplings.

Using the constitutive equation of co-rotational derivative type for anisotropic viscoelastic fluid-liquid crystalline(LC),polymer liquids was developed.Two relaxation times are introduced in the equation:λn represents relaxation of the normal-symmetric stress components;λs represents relaxation of the shear-unsymmetric stress components.A vibrational rotating flow in gap between cylinders with small amplitudes is studied for the anisotropic viscoelastic fluid-liquid crystalline polymer.The time-dependent constitutive equation are linearized with respect to parameter of small amplitude.For the normal-symmetric part of stress tensor analytical expression of the shear stress is obtained by the constitutive equation.The complex viscosity,complex shear modulus,dynamic and imaginary viscosities,storage modulus and loss modulus are obtained for the normal-symmetric stress case which are defined by the common shear rate.For the shear-unsymmetric stress part,two shear stresses are obtained thus two complex viscosities and two complex shear modulus(i.e.first and second one) are given by the constitutive equation which are defined by rotating shear rate introduced by author.The dynamic and imaginary viscosities,storage modulus and loss modulus are given for each complex viscosities and complex shear modulus.Using the constituive equation the rotating flow with small amplitudes in gap between two coaxial cylinders is studied.

A general analysis of poroelasticity for vertical transverse isotropy (VTI) shows that four eigenvectors are pure shear modes with no coupling to the pore-fluid mechanics. The remaining two eigenvectors are linear combinations of pure compression and uniaxial shear, both of which are coupled to the fluid mechanics. After reducing the problem to a 2 × 2 system, the analysis shows in a relatively elementary fashion how a poroelastic system with isotropic solid elastic frame, but with anisotropy introduced only through the poroelastic coefficients (and, therefore, termed soft anisotropy), interacts with the mechanics of the pore fluid and produces shear dependence on fluid properties in the overall poroelastic system. The analysis shows, for example, that this effect is always present (though sometimes small in magnitude) in the systems studied and can be comparatively large (on the order of 10 to 20 per cent) for wave propagation studies in some rocks, including Sierra White granite and Spirit River sandstone. Some of the results quoted here are obtained by using a new product formula relating local bulk and uniaxial shear energy to the product of the two eigenvalues that are coupled to the fluid mechanics. This product formula was first derived in prior work. The results obtained here are observed to be useful both for explaining difficult to reconcile laboratory wave propagation (especially ultrasonic) data showing that the shear modulus exhibits clear dependence on fluid content and also for benchmarking of poroelastic codes.

We perform experiments and numerical simulations to investigate spatial distribution of pressure in a sheared dilatant fluid of the Taylor-Couette flow under a constant external shear stress. In a certain range of shear stress, the flow undergoes the shear thickening oscillation around 20 Hz. The pressure measurement during the oscillation at the wall of the outer cylinder indicates that a localized negative pressure region rotates around the axis with the flow. The maximum negative pressure is close to the Laplace pressure of the grain radius and nearly independent of the applied shear stress. Simulations of a phenomenological model reveal that the thickened region is dominated by a negative pressure band, which extends along the tensile direction in the flow. Such shear thickening with negative pressure contradicts a naive picture of jamming mechanism, where thickening is expected in the compressing direction with the positive pressure.

The lining of normal lungs is covered by surfactants, because otherwise the surface tension of the aqueous layer would be too large to allow breathing. A lack of functioning surfactants can lead to respiratory distress syndrome, a potentially fatal condition in both premature infants and adults, and a major cause of death in the US and world-wide. We use a home-built Brewster angle microscope on an optically accessible deep channel viscometer to simultaneously observe the mesoscale structures of DPPC, the primary constituent of lung surfactant, on water surface and measure the interfacial velocity field. The measured interfacial velocity is compared to Navier-Stokes computations with the Boussinesq-Scriven surface model. Results show that DPPC monolayer behaves i) purely elastically at low surface pressures on water, ii) viscoelastically at modest surface pressures, exhibiting non-zero surface shear viscosity that is independent of the shear rate and flow inertia, and iii) at surface pressures approaching film collapse, DPPC loses its fluid characteristics, and a Newtonian surface model no longer captures its hydrodynamics.

Full Text Available Magnetorheological fluids (MRF, known for their variable shear stress contain magnetisable micrometer-sized particles (few micrometer to 200 micrometers in a nonmagnetic carrier liquid. To avoid settling of particles, smaller sized (3-10 micrometers particles are preferred, while larger sized particles can be used in MR brakes, MR clutches, etc. as mechanical stirring action in those mechanisms does not allow particles to settle down. Ideally larger sized particles provide higher shear stress compared to smaller sized particles. However there is need to explore the effect of particle sizes on the shear stress. In the current paper, a comparison of different particle sizes on MR effect has been presented. Particle size distributions of iron particles were measured using HORIBA Laser Scattering Particle Size Distribution Analyser. The particle size distribution, mean sizes and standard deviations have been presented. The nature of particle shapes has been observed using scanning electron microscopy. To explore the effect of particle sizes, nine MR fluids containing small, large and mixed sized carbonyl iron particles have been synthesized. Three concentrations (9%, 18% and 36% by volume for each size of particles have been used. The shear stresses of those MRF samples have been measured using ANTON PAAR MCR-102 Rheometer. With increase in volume fraction of iron particles, the MR fluids synthesized using “mixed sized particles” show better shear stress compared to the MR fluids containing “smaller sized spherical shaped particles” and “larger sized flaked shaped particles” at higher shear rate.

Cancer stem cells (CSCs), which are believed to be the source of tumor formation, are exposed to fluidshear stress as a result of blood flow within the blood vessels. It was theorized that CSCs would be less susceptible to cell death than non-CSCs after both types of cell were exposed to a fluidshear stress, and that higher levels of fluidshear stress would result in lower levels of cell viability for both cell types. To test this hypothesis, U87 glioblastoma cells were cultured adherently (containing smaller populations of CSCs) and spherically (containing larger populations of CSCs). They were exposed to fluidshear stress in a simulated blood flow through a 125-micrometer diameter polyetheretherketone (PEEK) tubing using a syringe pump. After exposure, cell viability data was collected using a BioRad TC20 Automated Cell Counter. Each cell type was tested at three physiological shear stress values: 5, 20, and 60 dynes per centimeter squared. In general, it was found that the CSC-enriched U87 sphere cells had higher cell viability than the CSC-depleted U87 adherent cancer cells. Interestingly, it was also observed that the cell viability was not negatively affected by the higher fluidshear stress values in the tested range. In future follow-up studies, higher shear stresses will be tested. Furthermore, CSCs from different tumor origins (e.g. breast tumor, prostate tumor) will be tested to determine cell-specific shear sensitivity. National Science Foundation Grant #1358991 supported the first author as an REU student.

Developing a shear thinning non-Newtonianfluid to substitute blood is desirable in studies of biomedicine engineering since blood is a shear thinning nonNewtonianfluid that exhibits both viscous and elastic properties, and generally not available in large volume. The rheological properties of aqueous Xanthan gum with different concentrations and temperatures were studied in present paper. The results show that aqueous Xanthan gum is a non-Newtonianfluid which displays remarkable shear thinning behaviour and is a suitable blood analog fluid. There is a power law distribution relationship between shear stress and shear rate, and the higher the solution concentration is, the more strongly it displays shear thinning behaviours. Viscosity values of aqueous Xanthan gum increase with the solution temperature decrease or with the solution concentration increase in linearity. Moreover at the temperature of 37℃, aqueous Xanthan gum with concentration of 0.4‰ and 0.6‰ matches human blood best in rheological properties. According to the resuits, the viscosity expression varied with temperature and concentrition is obtained, and the stability of Xanthan gum solution is discussed.

This work presents an experimental study on the heat transfer enhancement by means of a tube with wire-coil insert,for non-Newtonian laminar and transitional flow. The dimensionless pitch and wire diameter (based on the plain tube inner diameter) were chosen as p/D= 1 and e/D=0.09. Two pseudoplastic test fluids have been used: 1% by weight aqueous solutions of carboxymethyl cellulose (CMC) with high viscosity and medium viscosity. A wide range of flow conditions has been covered: Reynolds ...

A new technology, compression-assisted aggregation, is developed to enhance the strength of electrorheological (ER) fluids. The yield shear stress of ER fluids depends on the fluid microstructure. The unassisted electric-field induced ER structure mainly consists of single chains, whose weak points are at their ends. This new technology produces a structure consisting of robust thick columns with strong ends. As the weak points of the original ER structure are greatly enforced, the new structure makes ER fluids super-strong: At a moderate electric field and moderate pressure the yield shear stress of ER fluids at 35% volume fraction exceeds 100 kPa, well above any requirement for major industrial applications.

Full Text Available In this paper, an aqueous solution of xanthan gum (XG at a weight fraction as high as 0.2% was elected as the non-Newtonian base liquid, the multi-walled carbon nanotubes (MWCNTs dispersed into non-Newtonian XG aqueous at different weight factions of MWCNTs was prepared. Convection heat transfer of non-Newtonian nanofluids in the shell side of helical baffled heat exchanger combined with elliptic tubes has been investigated experimentally and numerically using single-phase flow model. Results showed that the enhancement of the convective heat transfer coefficient increases with an increase in the Reynolds number and the nanoparticle concentration. For nanofluids with 0.2 wt %, 0.5 wt % and 1.0 wt % MWCNTs, the Nusselt number, respectively, increases by 11%, 21% and 35% on average at the same Reynolds number, while the comprehensive thermal performance factors are 3%–5%, 15%–17% and 24%–26% higher than that of base fluid at the same volume rate. A remarkable heat transfer enhancement can be obtained by adding MWCNTs into XG aqueous solution based on thermal resistance analysis. Correlations have been suggested for the shell-side Nusselt number and friction factor of non-Newtonian nanofluids in the helical baffled heat exchanger with elliptic tubes. Good agreements existed between corrections and experimental data.

The viscosity of colloidal suspensions varies with shear rate, an important effect encountered in many natural and industrial processes. Although this non-Newtonian behavior is believed to arise from the arrangement of suspended particles and their mutual interactions, microscopic particle dynamics are difficult to measure. By combining fast confocal microscopy with simultaneous force measurements, we systematically investigate a suspension\\'s structure as it transitions through regimes of different flow signatures. Our measurements of the microscopic single-particle dynamics show that shear thinning results from the decreased relative contribution of entropic forces and that shear thickening arises from particle clustering induced by hydrodynamic lubrication forces. This combination of techniques illustrates an approach that complements current methods for determining the microscopic origins of non-Newtonian flow behavior in complex fluids.

In this study, the influence of the shear rate and shear time on the transient viscosity of polystyrene-ethylacrylate based shear thickening fluid (STF) is investigated. If the shear rate is stepwise changed, it is found that both the viscosity and critical shear rate are affected by the shear time. Above the critical shear rate, the viscosity of the STF with larger power law exponent (n) increases faster. However, the viscosity tends to decrease when the shear time is long enough. This phenomenon can be responsible for the reversible structure buildup and the break-down process. An effective volume fraction (EVF) mechanism is proposed to analyze the shear time dependent viscosity and it is found that viscosity changes in proportion to EVF. To further clarify the structure evolution, a structural kinetic model is studied because the structural kinetic parameter (λ) could describe the variation in the effective volume fraction. The theoretical results of the structural kinetic model agree well with the experimental results. With this model, the change in viscosity and EVF can be speculated from the variation of λ and then the structure evolution can be better illustrated.

A general analysis of poroelasticity for vertical transverse isotropy (VTI) shows that four eigenvectors are pure shear modes with no coupling to the pore-fluid mechanics. The remaining two eigenvectors are linear combinations of pure compression and uniaxial shear, both of which are coupled to the fluid mechanics. After reducing the problem to a 2 x 2 system, the analysis shows in a relatively elementary fashion how a poroelastic system with isotropic solid elastic frame, but with anisotropy introduced through the poroelastic coefficients, interacts with the mechanics of the pore fluid and produces shear dependence on fluid properties in the overall poroelastic system. The analysis shows for example that this effect is always present (though sometimes small in magnitude) in the systems studied, and can be quite large (on the order of 10 to 20%) for wave propagation studies in some real granites and sandstones, including Spirit River sandstone and Schuler-Cotton Valley sandstone. Some of the results quoted here are obtained by using a new product formula relating local bulk and uniaxial shear energy to the product of the two eigenvalues that are coupled to the fluid mechanics. This product formula was first derived in prior work, but is given a more intuitive derivation here. The results obtained here are observed to be useful both for explaining difficult to reconcile experimental data, and for benchmarking of poroelastic codes.

Although there are many excellent ways to present the principle of the classical calculus, the novel presentations probably lead most naturally to the development of the non-Newtonian calculi. In this paper we introduce vector spaces over real and complex non-Newtonian field with respect to the *-calculus which is a branch of non-Newtonian calculus. Also we give the definitions of real and complex inner product spaces and study Hilbert spaces which are special type of normed space and complet...

Theory and applications of non-Newtonian calculus have been evolving rapidly over the recent years. As numerical methods have a wide range of applications in science and engineering, the idea of the design of such numerical methods based on non-Newtonian calculus is self-evident. In this paper, the well-known Runge-Kutta method for ordinary differential equations is developed in the frameworks of non-Newtonian calculus given in generalized form and then tested for different generating functio...

Full Text Available This paper is devoted to investigating some characteristic features of weighted means and convex functions in terms of the non-Newtonian calculus which is a self-contained system independent of any other system of calculus. It is shown that there are infinitely many such useful types of weighted means and convex functions depending on the choice of generating functions. Moreover, some relations between classical weighted mean and its non-Newtonian version are compared and discussed in a table. Also, some geometric interpretations of convex functions are presented with respect to the non-Newtonian slope. Finally, using multiplicative continuous convex functions we give an application.

Differentiation and integration are basic operations of calculus and analysis. Indeed, they are many versions of the subtraction and addition operations on numbers, respectively. From 1967 till 1970 Michael Grossman and Robert Katz [1] gave definitions of a new kind of derivative and integral, converting the roles of subtraction and addition into division and multiplication, and thus establish a new calculus, called Non-Newtonian Calculus. So, in this paper, it is investigated to the convex functions and some inequalities in terms of Non-Newtonian Calculus. Then we compare with the Newtonian and Non-Newtonian Calculus.

We have conducted a real time, two-dimensional light scattering study of the nonlinear dynamics of field-induced structures in an electrorheological fluid subjected to oscillatory shear. We have developed a kinetic chain model of the observed dynamics by considering the response of a fragmenting/aggregating particle chain to the prevailing hydrodynamic and electrostatic forces. This structural theory is then used to describe the nonlinear rheology of ER fluids.

In this study, the immersed boundary-thermal lattice Boltzmann method has been used to simulate non-Newtonianfluid flow over a heated circular cylinder. The direct-forcing algorithm has been employed to couple the off-lattice obstacles and on-lattice fluid nodes. To investigate the effect of boundary sharpness, two different diffuse interface schemes are considered to interpolate the velocity and temperature between the boundary and computational grid points. The lattice Boltzmann equation with split-forcing term is applied to consider the effects of the discrete lattice and the body force to the momentum flux, simultaneously. A method for calculating the Nusselt number based on diffuse interface schemes is developed. The rheological and thermal properties of non-Newtonianfluids are investigated under the different power-law indices and Reynolds numbers. The effect of numerical parameters on the accuracy of the proposed method has been investigated in detail. Results show that the rheological and thermal properties of non-Newtonianfluids in the presence of a heated immersed body can be suitably captured using the immersed boundary thermal lattice Boltzmann method.

In the study the results of the friction factor in boundary layer and the distribution of heat transfer coefficient in non-Newtonian liquid agitated by different impellers, have been presented. It has been established that for studies in Na-CMC and guar gum aqueous solutions by the electrochemical method the following solution of 0.005 (kmol m{sup -3}) K{sub 3}[Fe(CN){sub 6}], 0.005 (kmol m{sup -3}) K{sub 4}[Fe(CN){sub 6}] and 0.3 (kmol m{sup -3}) K{sub 2}SO{sub 4} can be recommended. The common relationship (for a given type of an impeller) between local values of friction coefficient and heat transfer coefficient and Reynolds number proposed by Metzner and Otto [A.B. Metzner, R.E. Otto, Agitation of non-Newtonianfluids, AIChe J. 3 (1957) 3-10] for all power-law fluids, have been obtained. (author)

The lubrication performances of short journal bearings operating with non-Newtonian ferrofluids have been investigated in the present study. Based upon the ferrofluid model of Shliomis and the micro-continuum theory of Stokes, a two-dimensional modified Reynolds equation is derived by taking into account the effects of rotation of ferromagnetic particles and the effects of non-Newtonian properties. As an application, the short-bearing approximation is illustrated. Comparing with the conventional non-ferrofluid case, the short journal bearings with ferrofluids in the presence of magnetic fields result in a higher load capacity. Comparing with the Newtonian ferrofluid case, the non-Newtonian effects of couple stresses provide an enhancement in the load capacity, as well as a reduction in the friction parameter. The inclusion of non-Newtonian couple stresses signifies an improvement in performance characteristics of ferrofluid journal bearings. (orig.)

Full Text Available This paper is devoted to investigate some characteristic features of complex numbers and functions in terms of non-Newtonian calculus. Following Grossman and Katz, (Non-Newtonian Calculus, Lee Press, Piegon Cove, Massachusetts, 1972, we construct the field ℂ* of *-complex numbers and the concept of *-metric. Also, we give the definitions and the basic important properties of *-boundedness and *-continuity. Later, we define the space C*(Ω of *-continuous functions and state that it forms a vector space with respect to the non-Newtonian addition and scalar multiplication and we prove that C*(Ω is a Banach space. Finally, Multiplicative calculus (MC, which is one of the most popular non-Newtonian calculus and created by the famous exp function, is applied to complex numbers and functions to investigate some advance inner product properties and give inclusion relationship between C*(Ω and the set of C*′(Ω*-differentiable functions.

Full Text Available Theory and applications of non-Newtonian calculus have been evolving rapidly over the recent years. As numerical methods have a wide range of applications in science and engineering, the idea of the design of such numerical methods based on non-Newtonian calculus is self-evident. In this paper, the well-known Runge-Kutta method for ordinary differential equations is developed in the frameworks of non-Newtonian calculus given in generalized form and then tested for different generating functions. The efficiency of the proposed non-Newtonian Euler and Runge-Kutta methods is exposed by examples, and the results are compared with the exact solutions.

A kinetic model for characterizing the shear stress or shear strain rate of thixotropic materials is developed and combined with Oldroyd's viscoelastic model (1953) modified in this paper in order to predict the first normal stress difference. In order to test the method, transient and steady state data have been obtained with a Weissenberg rheogoniometer used to measure the constant stress and constant shear rate of a solution of polymethyl methacrylate in diethylphthalate. A computer was used to facilitate data acquisition.

Full Text Available An analysis is carried out to study the effect of heat and mass transfer on a non-Newtonian-fluid between two infinite parallel walls, one of them moving with a uniform velocity under the action of a transverse magnetic field. The moving wall moves with constant velocity in the direction of fluid flow while the free stream velocity is assumed to follow the exponentially increasing small perturbation law. Time-dependent wall suction is assumed to occur at permeable surface. The governing equations for the flow are transformed into a system of nonlinear ordinary differential equations by perturbation technique and are solved numerically by using the shooting technique with fourth order Runge-Kutta integration scheme. The effect of non-Newtonian parameter, magnetic pressure parameter, Schmidt number, Grashof number and modified Grashof number on velocity, temperature, concentration and the induced magnetic field are discussed. Numerical results are given and illustrated graphically for the considered Problem.

This paper is devoted to investigating some characteristic features of weighted means and convex functions in terms of the non-Newtonian calculus which is a self-contained system independent of any other system of calculus. It is shown that there are infinitely many such useful types of weighted means and convex functions depending on the choice of generating functions. Moreover, some relations between classical weighted mean and its non-Newtonian version are compared and discussed in a table...

This paper is devoted to investigate some characteristic features of complex numbers and functions in terms of non-Newtonian calculus. Following Grossman and Katz, (Non-Newtonian Calculus, Lee Press, Piegon Cove, Massachusetts, 1972), we construct the field ${\\Bbb C}^{\\ast}$ of ${\\ast}$ -complex numbers and the concept of ${\\ast}$ -metric. Also, we give the definitions and the basic important properties of ${\\ast}$ -boundedness and ${\\ast}$ -continuity. Later, we define the space ${C}_{\\ast}(...

The important point to note is that the non-Newtonian calculus is a self-contained system independent of any other system of calculus. Therefore the reader may be surprised to learn that there is a uniform relationship between the corresponding operators of this calculus and the classical calculus. Several basic concepts based on non-Newtonian calculus are presented by Grossman (1983), Grossman and Katz (1978), and Grossman (1979). Following Grossman and Katz, in the present paper, we introdu...

Computer simulations are presented of colloids, bidisperse in size, suspended in a shear-thinning viscoelastic fluid with the flow characteristics of a surfactant solution. The worm-like micelles are modeled in Responsive Particle Dynamics (RaPiD) as single soft particles obeying a generalized Brown

Many experiments have been conducted to study the hydrodynamic characteristics of column reactors and loop reactors. In this present work, a novel combined loop airlift fluidized bed reactor was developed to study the effect of superficial gas and liquid velocities, particle diameter, fluid properties on gas holdup by using Newtonian and non-Newtonian liquids. Compressed air was used as gas phase. Water, 5% n-butanol, various concentrations of glycerol (60 and 80%) were used as Newtonian liqu...

Recent observations of seismic slip occurring below the seismogenic zone of large fault zones have emphasized the significance of coeval ductile and brittle processes at high temperatures. We present observations of a shear zone contained within the Saddlebag Lake pendant of the eastern Sierra Nevada, CA, where Triassic and Jurassic metavolcanics and metasediments are highly strained in a high-temperature shear zone. Transposed bedding and cleavage that define a flattening fabric, dextrally rotated porphyroclasts, and a steep, pervasive lineation together suggest an overall transpressive kinematic regime for the ductile deformation. The high-strain rocks exhibit multiple episodes of vein formation, indicating a prolonged migration of hydrothermal fluids throughout the system. Crosscutting relationships and mineral assemblages define discrete sets of differently oriented veins. The veins form by fracture, but many veins are folded and boudinaged, showing synkinematic brittle and ductile deformation. We document foliation-parallel quartz veins that show shear displacement from the geometry of pull-apart structures and offsets of earlier veins. Synkinematic equilibrium mineral assemblages within the host rock and dynamic recrystallization of the quartz veins show they formed at temperatures around 400 to 500°C. The shear fractures have horizontal trace lengths of up to a few meters and displacements range from 2-3 mm to ~3 cm, with 1-5 mm of opening. Assuming the observed offset in the fractures occurred in a single event, these measurements are consistent with stress drops of 1 to 10 MPa. We interpret these observations to show that the veins formed as a result of high pore fluid pressure that caused shear failure at low effective stresses. Because foliated rocks are mechanically anisotropic, the foliation provided planes of weakness for failure with a preferred orientation. Evidence for shear failure occurring within crystal-plastic shear zones at high temperatures

This research looked for a method to determine the binary diffusion coefficient D of salts in liquids (especially in drilling fluids) not only accurately, but in a reasonable time. We chose to use the Taylor Dispersion Method. This technique has been used for measuring binary diffusion coefficients in gaseous, liquid and supercritical fluids, due to its simplicity and accuracy. In the method, the diffusion coefficient is determined by the analysis of the dispersion of a pulse of soluble material in a solvent flowing laminarly through a tube. This work describes the theoretical basis and the experimental requirements for the application of the Taylor Dispersion Method, emphasizing the description of our experiment. A mathematical formulation for both Newtonian and non-Newtonianfluids is presented. The relevant sources of errors are discussed. The experimental procedure and associated analysis are validated by applying the method in well known systems, such as NaCl in water.D of salts in liquids (especially in drilling fluids) not only accurately, but in a reasonable time. We chose to use the Taylor Dispersion Method. This technique has been used for measuring binary diffusion coefficients in gaseous, liquid and supercritical fluids, due to its simplicity and accuracy. In the method, the diffusion coefficient is determined by the analysis of the dispersion of a pulse of soluble material in a solvent flowing laminarly through a tube. This work describes the theoretical basis and the experimental requirements for the application of the Taylor Dispersion Method, emphasizing the description of our experiment. A mathematical formulation for both Newtonian and non-Newtonianfluids is presented. The relevant sources of errors are discussed. The experimental procedure and associated analysis are validated by applying the method in well known systems, such as NaCl in water. (author)

The miscible displacement of a shear-thinning fluid by another of same rheological properties is studied experimentally in a transparent fracture by an optical technique imaging relative concentration distributions. The fracture walls have complementary self-affine geometries and are shifted laterally in the direction perpendicular to the mean flow velocity {\\bf U} : the flow field is strongly channelized and macro dispersion controls the front structure for P\\'{e}clet numbers above a few units. The global front width increases then linearly with time and reflects the velocity distribution between the different channels. In contrast, at the local scale, front spreading is similar to Taylor dispersion between plane parallel surfaces. Both dispersion mechanisms depend strongly on the fluid rheology which shifts from Newtonian to shear-thinning when the flow rate increases. In the latter domain, increasing the concentration enhances the global front width but reduces both Taylor dispersion (due to the flattening...

Full Text Available A two-dimensional model is used to analyze the unsteady pulsatile flow of blood through a tapered artery with stenosis. The rheology of the flowing blood is captured by the constitutive equation of Carreau model. The geometry of the time-variant stenosis has been used to carry out the present analysis. The flow equations are set up under the assumption that the lumen radius is sufficiently smaller than the wavelength of the pulsatile pressure wave. A radial coordinate transformation is employed to immobilize the effect of the vessel wall. The resulting partial differential equations along with the boundary and initial conditions are solved using finite difference method. The dimensionless radial and axial velocity, volumetric flow rate, resistance impedance and wall shear stress are analyzed for normal and diseased artery with particular focus on variation of these quantities with non-Newtonian parameters.

This paper presents a series of numerical simulations of non-Newtonianfluids in high Reynolds number flows in circular pipes. The fluids studied in the computations have shear-thinning and yield stress properties. Turbulence is described using the Reynolds-Averaged Navier-Stokes (RANS) equations with the Boussinesq eddy viscosity hypothesis. The evaluation of standard, two-equation models led to some observations regarding the order of magnitude as well as probabilistic information about the rate of strain. We argue that an accurate estimate of the rate of strain tensor is essential in capturing important flow features. It is first recognised that an apparent viscosity comprises two flow dependant components: one originating from rheology and the other from the turbulence model. To establish the relative significance of the terms involved, an order of magnitude analysis has been performed. The main observation supporting further discussion is that in high Reynolds number regimes the magnitudes of fluctuating rates of strain and fluctuating vorticity dominate the magnitudes of their respective averages. Since these quantities are included in the rheological law, the values of viscosity obtained from the fluctuating and mean velocity fields are different. Validation against Direct Numerical Simulation data shows at least an order of magnitude discrepancy in some regions of the flow. Moreover, the predictions of the probabilistic analysis show a favourable agreement with statistics computed from DNS data. A variety of experimental, as well as computational data has been collected. Data come from the latest experiments by Escudier et al. [1], DNS from Rudman et al. [2] and zeroth-order turbulence models of Pinho [3]. The fluid rheologies are described by standard power-law and Herschel-Bulkley models which make them suitable for steady state calculations of shear flows. Suitable regularisations are utilised to secure numerical stability. Two new models have been

Blood non-Newtonian behavior on low-density lipoproteins (LDL) accumulation is analyzed numerically, while fluid-multilayered arteries are adopted for nonstenotic and 30%-60% symmetrical stenosed models. Present model considers non-Newtonian effects inside the lumen and within arterial layers simultaneously, which has not been examined in previous studies. Navier-Stokes equations are solved along with the mass transport convection-diffusion equations and Darcy’s model for species transport inside the luminal flow and across wall layers, respectively. Carreau model for the luminal flow and the modified Darcy equation for the power-law fluid within arterial layers are employed to model blood rheological characteristics, appropriately. Results indicate that in large arteries with relatively high Reynolds number Newtonian model estimates LDL concentration patterns well enough, however, this model seriously incompetent for regions with low WSS. Moreover, Newtonian model for plasma underestimates LDL concentration especially on luminal surface and across arterial wall. Therefore, applying non-Newtonian model seems essential for reaching to a more accurate estimation of LDL distribution in the artery. Finally, blood flow inside constricted arteries demonstrates that LDL concentration patterns along the stenoses inside the luminal flow and across arterial layers are strongly influenced as compared to the nonstenotic arteries. Additionally, among four stenosis severity grades, 40% stenosis is prone to more LDL accumulation along the post-stenotic regions.

The steady two-dimensional flow and heat transfer of a non-Newtonian power-law nanofluid over a stretching surface under convective boundary conditions and temperature-dependent fluid viscosity has been numerically investigated. The power-law rheology is adopted to describe non-Newtonian characteristics of the flow. Four different types of nanoparticles, namely copper (Cu), silver (Ag), alumina (Al 2 O 3) and titanium oxide (TiO 2) are considered by using sodium alginate (SA) as the base non-Newtonianfluid. Lie symmetry group transformations are used to convert the boundary layer equations into non-linear ordinary differential equations. The transformed equations are solved numerically by using a shooting method with fourth-order Runge-Kutta integration scheme. The results show that the effect of viscosity on the heat transfer rate is remarkable only for relatively strong convective heating. Moreover, the skin friction coefficient and the rate of heat transfer increase with an increase in Biot number.

The steady two-dimensional flow and heat transfer of a non-Newtonian power-law nanofluid over a stretching surface under convective boundary conditions and temperature-dependent fluid viscosity has been numerically investigated. The power-law rheology is adopted to describe non-Newtonian characteristics of the flow. Four different types of nanoparticles, namely copper (Cu), silver (Ag), alumina (Al$_2$O$_3$) and titanium oxide (TiO$_2$) are considered by using sodium alginate (SA) as the base non-Newtonianfluid. Lie symmetry group transformations are used to convert the boundary layer equations into non-linear ordinary differential equations. The transformed equations are solved numerically by using a shooting method with fourth-order Runge–Kutta integration scheme. The results show that the effect of viscosity on the heat transfer rate is remarkable only for relatively strong convective heating. Moreover, the skin friction coefficient and the rate of heat transfer increasewith an increase in Biot number.

This paper presents an experimental and computational study of air bubbles rising in a massecuite-equivalent non-Newtonian crystal suspension. The bubble trajectory inside the stagnant liquid of a 0.05% xanthan gum crystal suspension was investigated and modelled using the computational fluid dynamics (CFD) model to gain an insight into the bubble flow characteristics. The CFD code FLUENT was used for numerical simulation, and the bubble trajectory calculations were performed through a volume of fluid (VOF) model. The influences of the Reynolds number (Re), the Weber number (We) and the bubble aspect ratio (E) on the bubble trajectory are discussed. The conditions for the bubbles' path oscillations are identified. The experimental results showed that the path instability for the crystal suspension was less rapid than in water. The trajectory analysis indicated that 5.76 mm diameter bubbles followed a zigzag motion in the crystal suspension. Conversely, the smaller bubbles (5.76 mm) followed a path of least horizontal movement and larger bubbles (21.21 mm) produced more spiral motion within the crystal suspension. Path instability occurred for bubbles of 15.63 and 21.21 mm diameter, and they induced both zigzag and spiral trajectories within the crystal suspension. At low Re and We, smaller bubbles (5.76 mm) produced a zigzag trajectory, whereas larger bubbles (15.63 and 21.21 mm) showed both zigzag and spiral trajectories at intermediate and moderately high Re and We in the crystal suspension. The simulation results illustrated that a repeating pattern of swirling vortices was created for smaller bubbles due to the unstable wake and unsteady flow of these bubbles. This is the cause of the smaller bubbles moving in a zigzag way. Larger bubbles showed two counter-rotating trailing vortices at the back of the bubble. These vortices induced a velocity component to the gas-liquid interface and caused a deformation. Hence, the larger bubbles produced a path

In a wide range of applications, microfluidic channels are implemented in soft substrates. In such configurations, where fluidic inertia and compressibility are negligible, the propagation of fluids in channels is governed by a balance between fluid viscosity and elasticity of the surrounding solid. The viscous-elastic interactions between elastic substrates and non-Newtonianfluids are particularly of interest due to the dependence of viscosity on the state of the system. In this work, we study the fluid-structure interaction dynamics between an incompressible non-Newtonianfluid and a slender linearly elastic cylinder under the creeping flow regime. Considering power-law fluids and applying the thin shell approximation for the elastic cylinder, we obtain a nonhomogeneous p-Laplacian equation governing the viscous-elastic dynamics. We present exact solutions for the pressure and deformation fields for various initial and boundary conditions for both shear-thinning and shear-thickening fluids. We show that in contrast to Stokes' problem where a compactly supported front is obtained for shear-thickening fluids, here the role of viscosity is inversed and such fronts are obtained for shear-thinning fluids. Furthermore, we demonstrate that for the case of a step in inlet pressure, the propagation rate of the front has a tn/n +1 dependence on time (t ), suggesting the ability to indirectly measure the power-law index (n ) of shear-thinning liquids through measurements of elastic deformation.

the novel presentations probably lead most naturally to the development of the non-Newtonian calculi. In this paper we introduce vector spaces over real and complex non-Newtonian field with respect to the *-calculus which is a branch of non-Newtonian calculus. Also we give the definitions of real and complex inner product spaces and study Hilbert spaces which are special type of normed space and complete inner product spaces in the sense of *-calculus. Furthermore, as an example of Hilbert spaces, first we introduce the non-Cartesian plane which is a nonlinear model for plane Euclidean geometry. Secondly, we give Euclidean, unitary, and sequence spaces via corresponding norms which are induced by an inner product. Finally, by using the *-norm properties of complex structures, we examine Cauchy-Schwarz and triangle inequalities.

Full Text Available The important point to note is that the non-Newtonian calculus is a self-contained system independent of any other system of calculus. Therefore the reader may be surprised to learn that there is a uniform relationship between the corresponding operators of this calculus and the classical calculus. Several basic concepts based on non-Newtonian calculus are presented by Grossman (1983, Grossman and Katz (1978, and Grossman (1979. Following Grossman and Katz, in the present paper, we introduce the sets of bounded, convergent, null series and p-bounded variation of sequences over the complex field C* and prove that these are complete. We propose a quite concrete approach based on the notion of Köthe-Toeplitz duals with respect to the non-Newtonian calculus. Finally, we derive some inclusion relationships between Köthe space and solidness.

The important point to note is that the non-Newtonian calculus is a self-contained system independent of any other system of calculus. Therefore the reader may be surprised to learn that there is a uniform relationship between the corresponding operators of this calculus and the classical calculus. Several basic concepts based on non-Newtonian calculus are presented by Grossman (1983), Grossman and Katz (1978), and Grossman (1979). Following Grossman and Katz, in the present paper, we introduce the sets of bounded, convergent, null series and p-bounded variation of sequences over the complex field C* and prove that these are complete. We propose a quite concrete approach based on the notion of Köthe-Toeplitz duals with respect to the non-Newtonian calculus. Finally, we derive some inclusion relationships between Köthe space and solidness.

The rheological and heat-conduction constitutive models of micropolar fluids (MFs), which are important non-Newtonianfluids, have been, until now, characterized by simple linear expressions, and as a consequence, the non-Newtonian performance of such fluids could not be effectively captured. Here, we establish the novel nonlinear constitutive models of a micropolar fluid and apply them to boundary layer flow and heat transfer problems. The nonlinear power law function of angular velocity is represented in the new models by employing generalized "n-diffusion theory," which has successfully described the characteristics of non-Newtonianfluids, such as shear-thinning and shear-thickening fluids. These novel models may offer a new approach to the theoretical understanding of shear-thinning behavior and anomalous heat transfer caused by the collective micro-rotation effects in a MF with shear flow according to recent experiments. The nonlinear similarity equations with a power law form are derived and the approximate analytical solutions are obtained by the homotopy analysis method, which is in good agreement with the numerical solutions. The results indicate that non-Newtonian behaviors involving a MF depend substantially on the power exponent n and the modified material parameter K 0 introduced by us. Furthermore, the relations of the engineering interest parameters, including local boundary layer thickness, local skin friction, and Nusselt number are found to be fitted by a quadratic polynomial to n with high precision, which enables the extraction of the rapid predictions from a complex nonlinear boundary-layer transport system.

Full Text Available Many experiments have been conducted to study the hydrodynamic characteristics of column reactors and loop reactors. In this present work, a novel combined loop airlift fluidized bed reactor was developed to study the effect of superficial gas and liquid velocities, particle diameter, fluid properties on gas holdup by using Newtonian and non-Newtonian liquids. Compressed air was used as gas phase. Water, 5% n-butanol, various concentrations of glycerol (60 and 80% were used as Newtonian liquids, and different concentrations of carboxy methyl cellulose aqueous solutions (0.25, 0.6 and 1.0% were used as non-Newtonian liquids. Different sizes of spheres, Bearl saddles and Raschig rings were used as solid phases. From the experimental results, it was found that the increase in superficial gas velocity increases the gas holdup, but it decreases with increase in superficial liquid velocity and viscosity of liquids. Based on the experimental results a correlation was developed to predict the gas hold-up for Newtonian and non-Newtonian liquids for a wide range of operating conditions at a homogeneous flow regime where the superficial gas velocity is approximately less than 5 cm/s

Full Text Available An immersed boundary-lattice Boltzmann method is developed for fluid-structure interactions involving non-Newtonianfluids (e.g., power-law fluid. In this method, the flexible structure (e.g., capsule dynamics and the fluid dynamics are coupled by using the immersed boundary method. The incompressible viscous power-law fluid motion is obtained by solving the lattice Boltzmann equation. The non-Newtonian rheology is achieved by using a shear rate-dependant relaxation time in the lattice Boltzmann method. The non-Newtonian flow solver is then validated by considering a power-law flow in a straight channel which is one of the benchmark problems to validate an in-house solver. The numerical results present a good agreement with the analytical solutions for various values of power-law index. Finally, we apply this method to study the deformation of a capsule in a power-law shear flow by varying the Reynolds number from 0.025 to 0.1, dimensionless shear rate from 0.004 to 0.1, and power-law index from 0.2 to 1.8. It is found that the deformation of the capsule increases with the power-law index for different Reynolds numbers and nondimensional shear rates. In addition, the Reynolds number does not have significant effect on the capsule deformation in the flow regime considered. Moreover, the power-law index effect is stronger for larger dimensionless shear rate compared to smaller values.

A surface force apparatus was used to measure the transient and steady-state friction forces between molecularly smooth mica surfaces confining thin films of squalane, C{sub 30}H{sub 62}, a saturated, branched hydrocarbon liquid. The dynamic friction ''phase diagram'' was determined under different shearing conditions, especially the transitions between stick-slip and smooth sliding ''states'' that exhibited a chaotic stick-slip regime. The apparently very different friction traces exhibited by simple spherical, linear, and branched hydrocarbon films under shear are shown to be due to the much longer relaxation times and characteristic length scales associated with transitions from rest to steady-state sliding, and vice versa, in the case of branched liquids. The physical reasons and tribological implications for the different types of transitions observed with spherical, linear, and branched fluids are discussed.

In the present study, entropy production in ﬂow ﬁelds due to slider bearings is formulated. The rate of entropy generation is computed for different ﬂuid properties and geometric conﬁgurations of the slider bearing. In order to account for the non-Newtonian effect, a special type of third-grade ﬂuid is considered. It is found that the rate of entropy generation is inﬂuenced signiﬁcantly by the height of the bearing clearance and the non-Newtonian parameter of the ﬂuid.

Electrospinning uses an external electrostatic field to accelerate and stretch a charged polymer jet, and may produce ultrafine "nanofibers." Many polymers have been successfully electrospun in the laboratory. Recently Hohman [et al.] [Phys. Fluids, 13, 2201 (2001)] proposed an electrohydrodynamic model for electrospinning Newtonian jets. A problem arises, however, with the boundary condition at the nozzle. Unless the initial surface charge density is zero or very small, the jet bulges out upon exiting the nozzle in a "ballooning instability," which never occurs in reality. In this paper, we will first describe a slightly different Newtonian model that avoids the instability. Well-behaved solutions are produced that are insensitive to the initial charge density, except inside a tiny "boundary layer" at the nozzle. Then a non-Newtonian viscosity function is introduced into the model and the effects of extension thinning and thickening are explored. Results show two distinct regimes of stretching. For a "mildly stretched" jet, the axial tensile force in the fiber resists stretching, so that extension thinning promotes stretching and thickening hinders stretching. For a "severely stretched" jet, on the other hand, the tensile force enhances stretching at the beginning of the jet and suppresses it farther downstream. The effects of extensional viscosity then depend on the competition between the upstream and downstream dynamics. Finally, we use an empirical correlation to simulate strain hardening typical of polymeric liquids. This generally steepens the axial gradient of the tensile stress. Stretching is more pronounced at the beginning but weakens later, and ultimately thicker fibers are produced because of strain hardening.

A monoclonal antibody solution displays an increase in low shear rate viscosity upon aggregation after prolonged incubation at 40°C. The morphology and interactions leading to the formation of the aggregates responsible for this non-Newtonian character are resolved using small-angle neutron scattering. Our data show a weak repulsive barrier before proteins aggregate reversibly, unless a favorable contact with high binding energy occurs. Two types of aggregates were identified after incubation at 40°C: oligomers with radius of gyration ∼10 nm and fractal submicrometer particles formed by a slow reaction-limited aggregation process, consistent with monomers colliding many times before finding a favorable strong interaction site. Before incubation, these antibody solutions are Newtonian liquids with no increase in low shear rate viscosity and no upturn in scattering at low wavevector, whereas aggregated solutions under the same conditions have both of these features. These results demonstrate that fractal submicrometer particles are responsible for the increase in low shear rate viscosity and low wavevector upturn in scattered intensity of aggregated antibody solutions; both are removed from aggregated samples by filtering.

It is well known that density inhomogeneities at the solid-liquid interface can have a strong effect on the velocity profile of a nanoconfined fluid in planar Poiseuille flow. However, it is difficult to control the density inhomogeneities induced by solid walls, making this type of system...... systems. Using the sinusoidal transverse force method to produce shearing velocity profiles and the sinusoidal longitudinal force method to produce inhomogeneous density profiles, we are able to observe the interactions between the two property inhomogeneities at the level of individual Fourier components....... This gives us a method for direct measurement of the coupling between the density and velocity fields and allows us to introduce various feedback control mechanisms which customize fluid behavior in individual Fourier components. We briefly discuss the role of temperature inhomogeneity and consider whether...

Net population growth of some dinoflagellates is inhibited by fluidshear at shear stresses comparable with those generated during oceanic turbulence. Decreased net growth may occur through lowered cell division, increased mortality, or both. The dominant mechanism under various ...

We have developed an on-line computer-controlled sensor, based on ultrasound reflection measurements, to determine the product of the viscosity and density of a liquid or slurry for Newtonian fluids and the shear impedance of the liquid for non-Newtonianfluids. A 14 MHz shear wave transducer is bonded to one side of a 45-90 degrees fused silica wedge and the base is in contract with the liquid. Twenty-eight echoes were observed due to the multiple reflections of an ultrasonic shear horizontal (SH) wave within the wedge. The fast Fourier transform of each echo was obtained for a liquid and for water, which serves as the calibration fluid, and the reflection coefficient at the solid-liquid interface was obtained. Data were obtained for 11 sugar water solutions ranging in concentration from 10% to 66% by weight. The viscosity values are shown to be in good agreement with those obtained independently using a laboratory viscometer. The data acquisition time is 14s and this can be reduced by judicious selection of the echoes for determining the reflection coefficient. The measurement of the density results in a determination of the viscosity for Newtonian fluids or the shear wave velocity for non-Newtonianfluids. The sensor can be deployed for process control in a pipeline, with the base of the wedge as part of the pipeline wall, or immersed in a tank.

INSTAWILITY AT vin.. INTERFIACE I*.VWUN , TWO SUEARING FLUIDS IN A C|UANNEL Yuriko Renardy Mathematics Research Center University of Wisconsin-Madison...RESEARCH CENTER INSTABILITY AT THE INTERFACE BETWEEN TWO SHEARINGFLUIDS IN A CHANNEL Yuriko Renardy Technical Summary Report #2787 February 1985...INSTABILITY AT THE INTERFACE BETWEEN TWO SHEARINGFLUIDS IN A CHANNEL Yuriko Renardy 0 §1

This paper presents the homotopy series solution of the Navier-Stokes and energy equations for non-Newtonian flows. Three different problems, Couette flow, Poiseuille flow and Couette-Poiseuille flow have been investigated. For all three cases, the nonlinear momentum and energy equations have been solved using the homotopy method and analytical approximations for the velocity and the temperature distribution have been obtained. The current results agree well with those obtained by the homotopy perturbation method derived by Siddiqui et al (2008 Chaos Solitons Fractals 36 182-92). In addition to providing analytical solutions, this paper draws attention to interesting physical phenomena observed in non-Newtonian channel flows. For example, it is observed that the velocity profile of non-Newtonian Couette flow is indistinctive from the velocity profile of the Newtonian one. Additionally, we observe flow separation in non-Newtonian Couette-Poiseuille flow even though the pressure gradient is negative (favorable). We provide physical reasoning for these unique phenomena.

This paper is devoted to line and double integrals in the sense of non-Newtonian calculus (*-calculus). Moreover, in the sense of *-calculus, the fundamental theorem of calculus for line integrals and double integrals are stated and proved, and some applications are presented.

Full Text Available The blood flow through a tapered artery with a stenosis is analyzed, assuming the blood as tangent hyperbolic fluid model. The resulting nonlinear implicit system of partial differential equations is solved analytically with the help of perturbation method. The expressions for shear stress, velocity, flow rate, wall shear stress and longitudinal impedance are obtained. The variations of power law index m, Weissenberg number We, shape of stenosis n and stenosis size δ are discussed different type of tapered arteries.

Non-Newtonian ﬂuid ﬂow in a pipe system is considered and a third grade non-Newtonian ﬂuid is employed in the analysis. The velocity and temperature distributions across the pipe are presented. Entropy generation number due to heat transfer and ﬂuid friction is formulated. The inﬂuences of non-Newtonian parameter and Brinkman number on entropy generation number are examined. It is found that increasing the non-Newtonian parameter reduces the ﬂuid friction in the region close to the pipe wall. This in turn results in low entropy generation with increasing non-Newtonian parameter. Increasing Brinkman number enhances the ﬂuid friction and heat transfer rates; in which case, entropy number increases with increasing Brinkman number.

The dynamic response of the 57 vol./vol. % dense spherical silica particle-polyethylene glycol suspension at high pressure was investigated through short pulsed laser induced shock experiments. The measured back free surface velocities by a photonic Doppler velocimetry showed that the shock and the particle velocities decreased while the shock wave transmitted in the shear thickening fluid (STF), from which an equation of state for the STF was obtained. In addition, the peak stress decreased and the absorbed energy increased rapidly with increasing the thickness for a thin layer of the STF, which should be attributed to the impact-jammed behavior through compression of particle matrix, the deformation or crack of the hard-sphere particles, and the volume compression of the particles and the polyethylene glycol.

The forced vibration of a sandwich beam integrating a shear thickening fluid (STF) core and with conductive skins subjected to a periodic excitation was investigated theoretically in this study. The rheological properties of the STF material including viscosity, plasticity, and elasticity may be changed under the periodic vibration, and hence they were considered. The governing equation of motion was derived based on the complex stiffness method and some key parameters were derived based on the Timoshenko beam theory. Effects of the excitation frequency, the excitation amplitude, the excitation location, and the skin/core thickness ratio on the nature frequency of the sandwich beam were investigated. It was found that the STF core has a significant effect on the dynamic property of the sandwich beam. Based on the findings, integrating the STF core in a sandwich beam can reduce the vibration of the beam.

In this work the flow of the Oldroyd 8-constant fluid model in a scraped surface heat exchanger (SSHE) is studied. We have taken the steady incompressible isothermal flow of a fluid around a periodic arrangement of pivoted scraper blades in a channel for a generalized Poiseuille flow, and the flow is modeled using the lubrication-approximation theory (LAT), where as in SSHE the gaps between the blades and the device walls are narrow. Using these approximations we got the non-linear boundary value problem which is solved using the Adomian decomposition method. Expressions for velocity profiles for different regions, flow rates, stream function are obtained. Graphical and tabular representation for the velocity profile and for the different flow parameters involved is also incorporated. Foodstuffs behave as non-Newtonian material, possess shear-thinning and shear-thickening effects, so they are considered for the understanding of non-Newtonian effects inside the SSHE Oldroyd 8-constant fluid model. In addition to food industry this work will also be helpful in pharmaceutical and chemical industries as most of the materials used in the industry are non-Newtonian in nature.

Although there are five effective shear moduli for any layered VTI medium, one and only one effective shear modulus of the layered system (namely the uniaxial shear) contains all the dependence of pore fluids on the elastic or poroelastic constants that can be observed in vertically polarized shear waves. Pore fluids can increase the magnitude the shear energy stored in this modulus by an amount that ranges from the smallest to the largest effective shear moduli of the VTI system. But, since there are five shear moduli in play, the overall increase in shear energy due to fluids is reduced by a factor of about 5 in general. We can therefore give definite bounds on the maximum increase of overall shear modulus, being about 20% of the allowed range as liquid is fully substituted for gas. An attendant increase of density (depending on porosity and fluid density) by approximately 5 to 10% decreases the shear wave speed and, thereby, partially offsets the effect of this shear modulus increase. The final result is an increase of shear wave speed on the order of 5 to 10%. This increase is shown to be possible under most favorable circumstances - i.e. when the shear modulus fluctuations are large (resulting in strong anisotropy) and the medium behaves in an undrained fashion due to fluid trapping. At frequencies higher than seismic (such as sonic and ultrasonic waves for well-logging or laboratory experiments), resulting short response times also produce the requisite undrained behavior and, therefore, fluids also affect shear waves at high frequencies by increasing rigidity.

Non-Newtonian ﬂuid ﬂow in annular pipes is considered and the entropy generation due to ﬂuid friction and heat transfer in them is formulated. A third-grade ﬂuid is employed to account for the non-Newtonian effect, while the Reynolds model is accommodated for temperature-dependent viscosity. Closed-form solutions for velocity, temperature, and entropy ﬁelds are presented. It is found that entropy generation number increases with reducing non-Newtonian parameter, while it is the reverse for the viscosity parameter, which is more pronounced in the region close to the annular pipe inner wall.

In some cases, the most general linear operator between two sequence spaces is given by an infinite matrix. So the theory of matrix transformations has always been of great interest in the study of sequence spaces. In the present paper, we introduce the matrix transformations in sequence spaces over the field C* and characterize some classes of infinite matrices with respect to the non-Newtonian calculus. Also we give the necessary and sufficient conditions on an infinite matrix ...

The prior estimate and decay property of positive solutions are derived for a system of quasi-linear elliptic differential equations first. Hence, the result of non-existence for differential equation system of radially nonincreasing positive solutions is implied. By using this non-existence result, blow-up estimates for a class quasi-linear reaction-diffusion systems (non-Newtonian filtration systems ) are established, which extends the result of semi- linear reaction- diffusion ( Fujita type ) systems .

In this paper,we first find finite travelling-wave solutions,and then investigate the short time development of interfaces for non-Newtonian diffusion equations with strong absorption.We show that the initial behavior of the interface depends on the concentration of the mass of u(x,0) near x =0.More precisely,we find a critical value of the concentration,which separates the heating front of interfaces from the cooling front of them.

A study of the Weissenberg effect (rod climbing in a stirred system) based on nonequilibrium molecular dynamics (NEMD) is reported. Simulation results from a soft-sphere fluid are used to obtain a self-consistent free-surface profile of the fluid of finite compressibility undergoing Couette flow between concentric cylinders. A numerical procedure is then applied to calculate the height profile for a hypothetical fluid with thermophysical properties of the soft-sphere liquid and of a dense colloidal suspension. The height profile calculated is identified with shear thickening and the forms of the viscometric functions. The maximum climb occurs between the cylinders rather than at the inner cylinder.

A computational study of the flow of a non-Newtonian power law fluid on a spinning disc is considered here. The main goal of this work is to examine the effect of non-Newtonian nature of the fluid on the flow development and associated contact line instability. The governing mass and momentum balance equations are simplified using the lubrication theory. The resulting model equation is a fourth order non-linear PDE which describes the spatial and temporal evolutions of film thickness. The movement of the contact line is modeled using a constant angle slip model. To solve this moving boundary problem, a numerical method is developed using a Galerkin/finite element method based approach. The numerical results show that the spreading rate of the fluid strongly depends on power law exponent n. It increases with the increase in the shear thinning character of the fluid (n 1). It is also observed that the capillary ridge becomes sharper with the value of n. In order to examine the stability of these ridges, a linear stability theory is also developed for these power law fluids. The dispersion relationship depicting the growth rate for a given wave number has been reported and compared for different power-law fluids. It is found that the growth rate of the instability decreases as the fluid becomes more shear thinning in nature, whereas it increases for more shear thickening fluids.

Full Text Available Uniqueness of self-similar very singular solutions with compact support are proved for the non-Newtonian polytropic filtration equation with gradient absorption $$ \\frac{\\partial u}{\\partial t} =\\hbox{div}(|\

Full Text Available In this paper, a symmetry particle method, the smoothed particle hydrodynamics (SPH method, is extended to deal with non‐Newtonian fluids. First, the viscous liquid is modeled by a non‐Newtonian fluid flow and the variable viscosity under shear stress is determined by the Carreau‐Yasuda model. Then a pressure correction method is proposed, by correcting density error with individual stiffness parameters for each particle, to ensure the incompressibility of fluid. Finally, an implicit method is used to improve efficiency and stability. It is found that the nonNewtonian behavior can be well displayed in all cases, and the proposed SPH algorithm is stable and efficient.

Full Text Available The pulsatile flow of blood through stenosed arteries is analyzed by assuming the blood as a two-fluid model with the suspension of all the erythrocytes in the core region as a non-Newtonianfluid and the plasma in the peripheral layer as a Newtonian fluid. The non-Newtonianfluid in the core region of the artery is assumed as a (i Herschel-Bulkley fluid and (ii Casson fluid. Perturbation method is used to solve the resulting system of non-linear partial differential equations. Expressions for various flow quantities are obtained for the two-fluid Casson model. Expressions of the flow quantities obtained by Sankar and Lee (2006 for the two-fluid Herschel-Bulkley model are used to get the data for comparison. It is found that the plug flow velocity and velocity distribution of the two-fluid Casson model are considerably higher than those of the two-fluid Herschel-Bulkley model. It is also observed that the pressure drop, plug core radius, wall shear stress and the resistance to flow are significantly very low for the two-fluid Casson model than those of the two-fluid Herschel-Bulkley model. Hence, the two-fluid Casson model would be more useful than the two-fluid Herschel-Bulkley model to analyze the blood flow through stenosed arteries.

correlation used in the WTP design guide has been shown to be inaccurate for Hanford waste feed materials. The use of the Thomas (1979) correlation in the design guide is not conservative—In cases where 100% of the particles are smaller than 74 μm or particles are considered to be homogeneous due to yield stress forces suspending the particles the homogeneous fraction of the slurry can be set to 100%. In such cases, the predicted critical velocity based on the conservative Oroskar and Turian (1980) correlation is reduced to zero and the design guide returns a value from the Thomas (1979) correlation. The measured data in this report show that the Thomas (1979) correlation predictions often fall below that measured experimental values. A non-Newtonian deposition velocity design guide should be developed for the WTP— Since the WTP design guide is limited to Newtonian fluids and the WTP expects to process large quantities of such materials, the existing design guide should be modified address such systems. A central experimental finding of this testing is that the flow velocity required to reach turbulent flow increases with slurry rheological properties due to viscous forces dampening the formation of turbulent eddies. The flow becomes dominated by viscous forces rather than turbulent eddies. Since the turbulent eddies necessary for particle transport are not present, the particles will settle when crossing this boundary called the transitional deposition boundary. This deposition mechanism should be expected and designed for in the WTP.

Bone loss is a serious health problem. In vivo studies have found that mechanical stimulation may inhibit bone loss as elevated strain in bone induces osteogenesis, i.e. new bone formation. However, the exact relationship between mechanical environment and osteogenesis is less clear. Normal strain is considered as a prime stimulus of osteogenic activity; however, there are some instances in the literature where osteogenesis is observed in the vicinity of minimal normal strain, specifically near the neutral axis of bending in long bones. It suggests that osteogenesis may also be induced by other or secondary components of mechanical environment such as shear strain or canalicular fluid flow. As it is evident from the literature, shear strain and fluid flow can be potent stimuli of osteogenesis. This study presents a computational model to investigate the roles of these stimuli in bone adaptation. The model assumes that bone formation rate is roughly proportional to the normal, shear and fluidshear strain energy density above their osteogenic thresholds. In vivo osteogenesis due to cyclic cantilever bending of a murine tibia has been simulated. The model predicts results close to experimental findings when normal strain, and shear strain or fluidshear were combined. This study also gives a new perspective on the relation between osteogenic potential of micro-level fluidshear and that of macro-level bending shear. Attempts to establish such relations among the components of mechanical environment and corresponding osteogenesis may ultimately aid in the development of effective approaches to mitigating bone loss.

Using nonequilibrium molecular-dynamics simulation, we study the shear-rate dependence of pressure and potential energy in a liquid metal subjected to shear. We show that both thermodynamic properties vary according to a power law gamma[over ];{beta} of the shear rate gamma[over ] , in which the exponent beta is a simple linear function of temperature and density. Moreover, we establish that the coefficients for this linear law are the same as those previously obtained for a Lennard-Jones fluid by Ge [Phys. Rev. E 67, 061201 (2003)]. This is a strong indication that these coefficients, as well as the linear law for beta , could be applicable to any atomic fluid. It is also an important step toward the determination of a nonequilibrium equation of state, which would predict the value of pressure and energy of a shearingfluid for any state point and any value of the applied shear rate.

New heart valves and other cardiovascular assist systems have to be tested for hydrodynamic performance. In place of human blood simple model fluids like glycerol solutions are employed often due to ethical and practical reasons. But blood exhibits complex non-Newtonian and viscoelastic behaviour. Rheological blood properties are reviewed based on literature and own experimental results. Furthermore we studied polymer solutions with respect to blood-like flow behaviour. Rheology was assessed by means of the low shear rotational viscometer (LS 40, Mettler-Toledo, Switzerland) under stationary and dynamic shear conditions (variation of frequency and angular displacement).

Investigation of wall-liquid mass transfer and heat transfer phenomena with gas-Newtonian and non-Newtonianfluids in vertically helical coil reactor have been reported in this article. Experiments were conducted to investigate the effect of various dynamic and geometric parameters on mass and heat transfer coefficients in the helical coil reactor. The flow pattern-based heat and mass transfer phenomena in the helical coil reactor are highlighted at different operating conditions. The study covered a wide range of geometric parameters such as diameter of the tube (d t ), diameter of the coil (D c ), diameter of the particle (d p ), pitch difference (p/D c ) and concentrations of non-Newtonian liquid. The correlation models for the heat and mass transfer coefficient based on the flow pattern are developed which may be useful in process scale-up of the helical coil reactor for industrial application. The frictional drag coefficient was also estimated and analyzed by mass transfer phenomena based on the electrochemical method.

In some cases, the most general linear operator between two sequence spaces is given by an infinite matrix. So the theory of matrix transformations has always been of great interest in the study of sequence spaces. In the present paper, we introduce the matrix transformations in sequence spaces over the field ℂ(*) and characterize some classes of infinite matrices with respect to the non-Newtonian calculus. Also we give the necessary and sufficient conditions on an infinite matrix transforming one of the classical sets over ℂ(*) to another one. Furthermore, the concept for sequence-to-sequence and series-to-series methods of summability is given with some illustrated examples.

20; Until now, non-newtonian calculus, multiplicative calculus in particular, has been presented as a curiosity and is nearly ignored for the social scientists field. In this paper, after a brief presentation of this calculus, we try to show how it could be used to re-explore from another perspective classical economic theory, more particularly the economic growth and in the maximum likelihood method from statistics.; Jusqu'à présent, le calcul non-newtonien, calcul multiplicatif en particuli...

A novel numerical method to lubricate a conventional finite diameter conical(cylindrical bearing with a non-Newtonian lubricant, while adhering to the power-law model, is presented. The elastic deformation of bearing and varied viscosity of lubrication due to the pressure distribution of film thickness are also considered. Simulation results indicate that the normal load carrying capacity is more pronounced for higher values of flow behavior index n, higher eccentricity ratios and larger misalignment factors. It is found that the viscosity-pressure to the effect of lubricant viscosity is significant.

Based upon a new mixed variational formulation for the three-field Stokes equations and linearized Non-Newtonian flow, an h -p finite element method is presented with or without a stabilization. As to the variational formulation without stabilization, optimal error bounds in h as well as in p are obtained. As with stabilization, optimal error bounds are obtained which is optimal in h and one order deterioration in p for the pressure, that is consistent with numerical results in [9, 12] and therefore solved the problem therein.Moreover, we proposed a stabilized formulation which is optimal in both h and p.

The study of non-Newtonian flow in plate heat exchangers (PHEs) is of great importance for the food industry. The objective of this work was to study the pressure drop of pineapple juice in a PHE with 50º chevron plates. Density and flow properties of pineapple juice were determined and correlated with temperature (17.4 < T < 85.8ºC) and soluble solids content (11.0 < Xs < 52.4 ºBrix). The Ostwald-de Waele (power law) model described well the rheological behavior. The friction factor for non-...

A theoretical model based on BCT lattice structure was developed.Resultant force in the BCT lattice structure was deduced,following the interaction force of two kinds of magnetic particles.According to empirical FroHlich-Kennelly law,the relationship between the magnetic induction and the magnetic field was discussed,and a predictive formula of shear stresses of the BCT lattice structure model was established for the case of small shear deformation.Compared with the experimental data for different particle volume fractions,the theoretical results of the shear stress indicate the effects of the saturation magnetization and the external magnetic field on the shear stress.

Understanding non-Darcian flow of shear-thinning fluids through rough-walled rock fractures is of vital importance in a number of industrial applications such as hydrogeology or petroleum engineering. Different laws are available to express the deviations from linear Darcy law due to inertial pressure losses. In particular, Darcy's law is often extended through addition of quadratic and cubic terms weighted by two inertial coefficients depending on the strength of the inertia regime. The relations between the effective shear viscosity of the fluid and the apparent viscosity in porous media when inertial deviations are negligible were extensively studied in the past. However, only recent numerical works have investigated the superposition of both inertial and shear-thinning effects, finding that the same inertial coefficients obtained for non-Darcian Newtonian flow applied in the case of shear-thinning fluids. The objective of this work is to experimentally validate these results, extending their applicability to the case of rough-walled rock fractures. To do so, flow experiments with aqueous polymer solutions have been conducted using replicas of natural fractures, and the effects of polymer concentration, which determine the shear rheology of the injected fluid, have been evaluated. Our findings show that the experimental pressure loss-flow rate data for inertial flow of shear-thinning fluids can be successfully predicted from the empirical parameters obtained during non-Darcian Newtonian flow and Darcian shear-thinning flow in a given porous medium.

Full Text Available In this study, the pseudo plastic model is used to obtain the solution for the steady thin film flow on the outer surface of long vertical cylinder for lifting and drainage problems. The non-linear governing equations subject to appropriate boundary conditions are solved analytically for velocity profiles by a modified homotopy perturbation method called the Optimal Homotopy Asymptotic method. Expressions for the velocity profile, volume flux, average velocity, shear stress on the cylinder, normal stress differences, force to hold the vertical cylindrical surface in position, have been derived for both the problems. For the non-Newtonian parameter β=0, we retrieve Newtonian cases for both the problems. We also plotted and discussed the affect of the Stokes number St, the non-Newtonian parameter β and the thickness δ of the fluid film on the fluid velocities.

Numerous natural processes are contingent on microorganisms' ability to swim through fluids with non-Newtonian rheology. Here, we use the model organism Caenorhabditis elegans and tracking methods to experimentally investigate the dynamics of undulatory swimming in shear-thinning fluids. Theory and simulation have proposed that the cost of swimming, or mechanical power, should be lower in a shear-thinning fluid compared to a Newtonian fluid of the same zero-shear viscosity. We aim to provide an experimental investigation into the cost of swimming in a shear-thinning fluid from (i) an estimate of the mechanical power of the swimmer and (ii) the viscous dissipation rate of the flow field, which should yield equivalent results for a self-propelled low Reynolds number swimmer. We find the cost of swimming in shear-thinning fluids is less than or equal to the cost of swimming in Newtonian fluids of the same zero-shear viscosity; furthermore, the cost of swimming in shear-thinning fluids scales with a fluid's effective viscosity and can be predicted using fluid rheology and simple swimming kinematics. Our results agree reasonably well with previous theoretical predictions and provide a framework for understanding the cost of swimming in generalized Newtonian fluids.

Dinoflagellate can be stimulated bioluminescence by hydrodynamic agitation. Two typical dinoflagellate (Lingulodinium polyedrum and Pyrocystis noctiluca) was choosed to research stimulated bioluminescence. The bioluminescence intensity and shear stress intensity were measured using fully developed pipe flow. There is shear stress threshold to agitate organism bioluminescence. From these experiment, the response thresholds of the stimulated bioluminscence always occurred in laminar flows at a shear stress level of 0.6-3 dyn/cm{sup 2}. At the same time, the spectral characteristc of dinoflagellate was recorded, the wavelength of them is about 470nm, and the full width at half maximum is approximate 30nm.

Full Text Available The gas holdup was studied in non-newtonian liquids in a gas-liquid and gas-liquid-solid reciprocating plate bioreactor. Aqueous solutions of carboxy methyl cellulose (CMC; Lucel, Lučane, Yugoslavia of different degrees of polymerization (PP 200 and PP 1000 and concentration (0,5 and 1%, polypropylene spheres (diameter 8.3 mm; fraction of spheres: 3.8 and 6.6% by volume and air were used as the liquid, solid and gas phase. The gas holdup was found to be dependent on the vibration rate, the superficial gas velocity, volume fraction of solid particles and Theological properties of the liquid ohase. Both in the gas-liquid and gas-liquid-solid systems studied, the gas holdup increased with increasing vibration rate and gas flow rate. The gas holdup was higher in three-phase systems than in two-phase ones under otter operating conditions being the same. Generally the gas holdup increased with increasing the volume fraction of solid particles, due to the dispersion action of the solid particles, and decreased with increasing non-Newtonian behaviour (decreasing flow index i.e. with increasing degree of polymerization and solution concentration of CMC applied, as a result of gas bubble coalescence.

An experimental description of the flow structure of non-Newtonian slurries in the laminar, transitional, and fully-developed turbulent pipe flow regimes was the primary objective of this research. Experiments were conducted in a large-scale pipe slurry flow facility with an inside diameter of 51 mm (2 inches). Approximately, 550 liters (145 gal) of slurry were necessary in the operation of the loop. Detailed velocity profile measurements by a two-color, two-component laser Doppler anemometer (LDA) were accomplished in a transparent test section with an optically transparent slurry. These velocity measurements were apparently the first ever reported for a non-Newtonian slurry with a yield value. The transparent slurry was formulated for these experiments from silica with a particle size of one to two microns, mineral oil, and Stoddard solvent. From linear regression analysis of concentric-cylinder viscometer data, the slurry exhibited yield-power-law behavior with a yield stress of 100 dynes/cm(sup 2), and an exponent of 0.630 for a solids concentration of 5.65 percent by weight. Good agreement was attained with rheological data derived from the pressure drop data in the flow loop under laminar flow conditions. The rheological properties of the transparent slurry were similar to many industrial slurries, including coal slurries, which have a yield value.

The Vortex Fluidic Device (VFD) is a rapidly rotating tube that can operate under continuous flow with a jet feeding liquid reactants to the tube's hemispherical base. It is a new 'green' approach to the organic synthesis with many industrial applications in cosmetics, protein folding and pharmaceutical production. The rate of reaction in the VFD is enhanced when the collision rate is increased. The aim of the project is to explain the fluid mechanics and optimize the performance of the device. One contribution to the increased yield is believed to be the high levels of shear stress. We attempt to enhance the shear stress by achieving high velocity gradients in the boundary layers. Another factor is the uncontrolled vibrations due to imperfections in the bearings and therefore it is important to assess their influence in the initial spreading. The surface area of the film should be maximized with respect to the rotation rate, geometry and orientation of the tube, flow rate, wettability and contact line dynamics. Experiments are presented for a flat disk and a curved bowl, establishing the optimum height of release, rotation rate and tube orientation. Vibrations were imposed to investigate the changes in the film formation. We discuss the implications of our results in the VFD.

Based on a mesoscopic theory we investigate the nonequilibrium dynamics of a sheared nematic liquid, with the control parameter being the shear stress σ xy (rather than the usual shear rate, γ). To this end we supplement the equations of motion for the orientational order parameters by an equation for γ, which then becomes time dependent. Shearing the system from an isotropic state, the stress-controlled flow properties turn out to be essentially identical to those at fixed γ. Pronounced differences occur when the equilibrium state is nematic. Here, shearing at controlled γ yields several nonequilibrium transitions between different dynamic states, including chaotic regimes. The corresponding stress-controlled system has only one transition from a regular periodic into a stationary (shear-aligned) state. The position of this transition in the σ xy-γ plane turns out to be tunable by the delay time entering our control scheme for σ xy. Moreover, a sudden change in the control method can stabilize the chaotic states appearing at fixed γ.

The current study investigates the drop characteristics of three Carboxymethylcellulose (CMC) sprays produced by the impingement of two liquid jets. The three water-based solutions used in this work (0.5 wt.-% CMC-7MF, 0.8 wt.-% CMC-7MF, and 1.4 wt.-% CMC-7MF) exhibited strong shear-thinning, non-Newtonian behavior - characterized by the Bird-Carreau rheological model. A generalized Bird-Carreau jet Reynolds number was used as the primary parameter to characterize the drop size and the drop velocity, which were measured using Phase Doppler Anemometry (PDA). PDA optical configuration enabled a drop size measurement range of approximately 2.3 to 116.2 μm. 50,000 drops were measured at each test condition to ensure statistical significance. The arithmetic mean diameter (D10) , Sauter mean diameter (D32) , and mass median diameter (MMD) were used as representative diameters to characterize drop size. The mean axial drop velocity Uz -mean along with its root-mean square Uz -rms were used to characterize drop velocity. Incredibly, measurements for all three CMC liquids and reference DI water sprays seemed to follow a single curve for D32 and MMD drop diameters in the high generalized Bird-Carreau jet Reynolds number range considered in this work (9.21E +03

The fractional calculus approach in the constitutive relationship model of viscoelastic fluid is introduced. The flow near a wall suddenly set in motion is studied for a non-Newtonian viscoelastic fluid with the fractional Maxwell model. Exact solutions of velocity and stress are obtained by using the discrete inverse Laplace transform of the sequential fractional derivatives. It is found that the effect of the fractional orders in the constitutive relationship on the flow field is significant. The results show that for small times there are appreciable viscoelastic effects on the shear stress at the plate, for large times the viscoelastic effects become weak.

The fractional calculus approach in the constitutive relationship model of viscoelastic fluid is introduced. The flow near a wall suddenly set in motion is studied for a non-Newtonian viscoelastic fluid with the fractional Maxwell model. Exact solutions of velocity and stress are obtained by using the discrete inverse Laplace transform of the sequential fractional derivatives. It is found that the effect of the fractional orders in the constitutive relationship on the flow field is significant. The results show that for small times there are appreciable viscoelastic effects on the shear stress at the plate, for large times the viscoelastic effects become weak.

The swimming behavior of microorganisms can be strongly affected by the rheology of their fluidic environment. In this talk, we experimentally investigate the swimming behavior of the nematode Caenorhabditis elegans (~1 mm length, 80 μm diameter) in shear-thinning fluids using tracking and velocimetry methods. We find substantial differences in the resulting flow fields between the shear-thinning and Newtonian cases, even though the swimming kinematics (e.g. speed and frequency) remain similar. For example, velocimetry data show that shear-thinning viscosity enhances vorticity and increases circulation near the strongest body vortex, located near the head of the nematode. These findings are in good agreement with recent theoretical and numerical results. We then estimate the local viscosity around the swimmer, measure the spatial decay of the flow field, and estimate the mechanical power (i.e. viscous dissipation) due to the worm's motion in shear-thinning fluids. We find that the flow decays more slowly in shear-thinning fluids than in Newtonian fluids, but the resulting mechanical power is approximately the same for swimming in shear-thinning fluids when compared to the Newtonian case.

The relaxation of non-Newtonian liquids with non-power-law rheology on partially wetted surfaces is rarely investigated. This study assesses the relaxation behavior of 14 partial wetting systems with non-power-law fluids by sessile drop method. These systems are two carboxymethylcellulose sodium solutions on two kinds of slides, cover glass, and silicon wafer surfaces; three polyethylene glycol (PEG400) + silica nanoparticle suspensions on polymethyl methacrylate and polystyrene surfaces. The dynamic contact angle and moving velocity of contact line relationship data for relaxation drops of the 14 tested systems demonstrate a power-law fluid-like behavior, and the equivalent power exponent for a certain fluid on different solid substrates are uniform. By analyzing the relationship between the equivalent power exponent and shear rate, it is proposed that a fluid regime with shear rates of a few tens of s controls relaxation dynamics.

Full Text Available In this study, a regular perturbation technique is utilized to derive the modified Reynolds equation which is applicable to power-law lubricant. The performance of slider bearings including pressure distributions, velocity distributions, film thickness, load capacity, flow rate, shear force, and friction coefficient is also derived analytically for various ξ, flow indices (n, and outlet film thicknesses (H0. These analytical solutions are clear to find the effects of the operation parameters rather than numerical methods. It can be simply and fast used for engineers. Subsequently, these proposed analytical solutions are used to analyze the lubrication performance of slider bearing with the power-law fluids.

Osteoarthritis is a common, localized joint disease that causes pain, stiffness and reduced mobility. Osteoarthritis is particularly common in the knees. The effects of osteoarthritis on the rheology of synovial fluid in the knees are not fully understood and consequently require further study. The purpose of this study is to investigate the effects of protein content on synovial fluidshear rheology. A secondary study outcome will include study of the temperature dependence of synovial fluid behaviour. 38 osteoarthritic synovial fluid samples were studied under shear flow. Shear properties were correlated with protein concentration. Viscosupplement was used as a comparison and to verify measurement reliability. The effects of temperature were investigated at 20, 29 and 37°C. Shear rheological properties were found to vary widely between samples, however all samples demonstrated clear non-Newtonianshear thinning behaviour. In general viscoelastic properties were lower in osteoarthritic samples than previously studied healthy synovial fluid. A moderate correlation was observed between synovial fluid dynamic moduli at a frequency of 2.5 Hz and protein concentration. Temperature was found to affect the rheology of osteoarthritic synovial fluid and was fitted with the Arrhenius model. Increased protein concentration has been correlated with decreased shear rheological parameters. Temperature dependence of synovial fluid was also demonstrated and modelled for use in Part 2 of this article.

A major issue with in situ subsurface remediation is the ability to achieve an even spatial distribution of remedial amendments to the contamination zones in an aquifer or vadose zone. Delivery of amendment to the aquifer using shear thinning fluid and to the vadose zone using aqueous foam has the potential to enhance the amendment distribution into desired locations and improve the remediation. 2-D saturated flow cell experiments were conducted to evaluate the enhanced sweeping, contaminant removal, and amendment persistence achieved by shear thinning fluid delivery. Bio-polymer xanthan gum solution was used as the shear thinning fluid. Unsaturated 1-D column and 2-D flow cell experiments were conducted to evaluate the mitigation of contaminant mobilization, amendment uniform distribution enhancement, and lateral delivery improvement by foam delivery. Surfactant sodium lauryl ether sulfate was used as the foaming agent. It was demonstrated that the shear thinning fluid injection enhanced the fluid sweeping over a heterogeneous system and increased the delivery of remedial amendment into low-permeability zones. The persistence of the amendment distributed into the low-perm zones by the shear thinning fluid was prolonged compared to that of amendment distributed by water injection. Foam delivery of amendment was shown to mitigate the mobilization of highly mobile contaminant from sediments under vadose zone conditions. Foam delivery also achieved more uniform amendment distribution in a heterogeneous unsaturated system, and demonstrated remarkable increasing in lateral distribution of the injected liquid compared to direct liquid injection.

The flows of non-Newtonian slurries, often suspensions of noncolloidal particles in yield stress fluids, are ubiquitous in many natural phenomena and industrial processes. Investigating the microstructure is essential allowing the refinement of macroscopic equations for complex suspensions. One important constraint on the dynamics of a Stokesian suspension is reversibility, which is not necessarily valid for complex fluids. The interaction of two particles in a reversing shear flow of complex fluids is a guide to understand the behavior of complex suspensions. We study the hydrodynamic interaction of two small freely-moving spheres in a linear flow field of yield stress fluids. An important point is that non-Newtonianfluid effects can be varied and unusual. Depending on the shear rate, even a yield stress fluid might show hysteresis, shear banding and elasticity at the local scales that need to be taken into account. We study these effects with the aid of conventional rheometry, Particle Image Velocimetry and Particle Tracking Velocimetry in an original apparatus. We show our preliminary experimental results. NSF.

We report the first real-time observations of the entire fully developed laminar secondary flow field of aqueous 2% Viscarin GP-209NF (a λ-carrageenan polysaccharide) in a square duct as made using a modest rheological NMR imaging (rheo-NMR) apparatus. Simulations using the Reiner-Rivlin constitutive equation verify the results. An included rheo-NMR flow rate quantification study assesses the measurement precision. Rheo-NMR resolves slow flows superimposed on primary flows about 300 times greater, making it a universally accessible technique by which full secondary flow field data may be systematically gathered.

which incLudes stress accumulation with fading memory was employed by Fogler and Goddard (1970. 1971), who specified a relaxation modulus (memory... Fogler and Goddard present large elastic effects, i.e. changes in the R(t) profiles, but for parameter values which minimize surface 1’ .1 23 tension...also on its appropriate time derivative in a differential model or on the pertinent past values for an Integral equation. Follow- ing Fogler and

in the tape casting process is modeled numerically with ANSYS FLUENT in combination with an Ostwald-de Waele power law constitutive equation. Based on rheometer experiments, the constants in the Ostwald-de Waele power law are identified for the considered LSM material and applied in the numerical modeling...

A polymer solution partially filling a rotating horizontal drum undergoes an elastically driven instability at low Reynolds numbers. This instability manifests itself through localized plumelike bursts, perturbing the free liquid surface. Here we present an expanded experimental account regarding the dynamics of individual plumes and the statistics pertaining to the complex collective interaction between plumes, which leads to plume coagulation. We also present a detailed description of an optical technique that enables the visualization and measurement of surface perturbations in coating flows within a rotating horizontal drum.

Fouling is the main bottleneck of the widespread of MBR systems. One way to decrease and/or control fouling is by process hydrodynamics. This can be achieved by the increase of liquid crossflow velocity. In rotational cross-flow MBR systems, this is attained by the spinning of e.g. impellers. Val...... as function of the angular velocity and the total suspended solids concentration....

Full Text Available This study was to investigate the hemodynamic effect of simulated plaques in left coronary artery models, which were generated from a sample patient’s data. Plaques were simulated and placed at the left main stem and the left anterior descending (LAD to produce at least 60% coronary stenosis. Computational fluid dynamics analysis was performed to simulate realistic physiological conditions that reflect the in vivo cardiac hemodynamics, and comparison of wall shear stress (WSS between Newtonian and non-Newtonianfluid models was performed. The pressure gradient (PSG and flow velocities in the left coronary artery were measured and compared in the left coronary models with and without presence of plaques during cardiac cycle. Our results showed that the highest PSG was observed in stenotic regions caused by the plaques. Low flow velocity areas were found at postplaque locations in the left circumflex, LAD, and bifurcation. WSS at the stenotic locations was similar between the non-Newtonian and Newtonian models although some more details were observed with non-Newtonian model. There is a direct correlation between coronary plaques and subsequent hemodynamic changes, based on the simulation of plaques in the realistic coronary models.

Numerous natural processes are contingent on microorganisms' ability to swim through fluids with non-Newtonian rheology. Here, we use the model organism Caenorhabditis elegans and tracking methods to experimentally investigate the dynamics of undulatory swimming in shear-thinning fluids. Theory and simulation have proposed that the cost of swimming, or mechanical power, should be lower in a shear-thinning fluid compared to a Newtonian fluid of the same zero-shear viscosity. We aim to provide an experimental investigation into the cost of swimming in a shear-thinning fluid from (i) an estimate of the mechanical power of the swimmer and (ii) the viscous dissipation rate of the flow field, which should yield equivalent results for a self-propelled low Reynolds number swimmer. We find the cost of swimming in shear-thinning fluids is less than or equal to the cost of swimming in Newtonian fluids of the same zero-shear viscosity; furthermore, the cost of swimming in shear-thinning fluids scales with a fluid's effec...

The convective flow of third grade non-Newtonian nanofluid through porous coaxial cylinders with inclined magnetic field is investigated. The governing partial differential equations are transformed to a system of nonlinear ordinary differential equations using the non-dimensional quantities. The transformed system of nonlinear ordinary differential equations is solved numerically using the fourth-order Runge-Kutta method. The viscosity of the nanofluid is considered as a function of temperature in form of Vogel's model. Numerical solutions are obtained for the velocity, temperature and nanoparticles concentration. The effects of the some physical parameters particularly the angle of inclination, the magnetic, Brownian motion and thermophoresis parameters on non-dimensional velocity, temperature and nanoparticles concentration are analyzed. It is found that as the angle of inclination of magnetic field increases, the velocity decreases. The results also show that increasing the thermophoresis parameter and Brownian motion, the temperature increases. By increasing the Brownian motion or decreasing the thermophoresis parameter, nanoparticles concentration increases.

The fully developed time-dependent flow of an incompressible, thermodynamically compatible non-Newtonian third-grade nanofluid is investigated. The classical Stokes model is considered in which the flow is generated due to the motion of the plate in its own plane with an impulsive velocity. The Lie symmetry approach is utilised to convert the governing nonlinear partial differential equation into different linear and nonlinear ordinary differential equations. The reduced ordinary differential equations are then solved by using the compatibility and generalised group method. Exact solutions for the model equation are deduced in the form of closed-form exponential functions which are not available in the literature before. In addition, we also derived the conservation laws associated with the governing model. Finally, the physical features of the pertinent parameters are discussed in detail through several graphs.

Full Text Available The study of non-Newtonian flow in plate heat exchangers (PHEs is of great importance for the food industry. The objective of this work was to study the pressure drop of pineapple juice in a PHE with 50º chevron plates. Density and flow properties of pineapple juice were determined and correlated with temperature (17.4 < T < 85.8ºC and soluble solids content (11.0 < Xs < 52.4 ºBrix. The Ostwald-de Waele (power law model described well the rheological behavior. The friction factor for non-isothermal flow of pineapple juice in the PHE was obtained for diagonal and parallel/side flow. Experimental results were well correlated with the generalized Reynolds number (20 < Re g < 1230 and were compared with predictions from equations from the literature. The mean absolute error for pressure drop prediction was 4% for the diagonal plate and 10% for the parallel plate.